k | Πm=1∞(1-qm)k |
1 | 1-q-q2+q5+q7-q12-q15+q22+q26-q35-q40+q51+q57-q70-q77+q92+q100+O(q101) |
2 | 1-2q-q2+2q3+q4+2q5-2q6-2q8-2q9+q10+2q13+3q14-2q15+2q16-2q19-2q20-2q23-q24+2q26+2q27 -2q28+2q29+q30+2q31+2q33-2q34-2q35+2q36-2q38-4q40+q44-2q45+2q48+2q50+2q51+q52-2q53 +2q55+2q56-2q59-2q61-2q63+2q64-4q66-2q69-q70+2q71+2q73-2q77+2q78+4q79+q80+2q83-2q84 +2q85-2q86+2q89-2q91-2q93-2q94-2q96+2q100+O(q101) |
3 | 1-3q+5q3-7q6+9q10-11q15+13q21-15q28+17q36-19q45+21q55-23q66+25q78-27q91+O(q101) |
4 | 1-4q+2q2+8q3-5q4-4q5-10q6+8q7+9q8+14q10-16q11-10q12-4q13-8q15+14q16+20q17+2q18 -11q20+20q21-32q22-16q23-4q25+14q26+8q27-9q28+20q29+26q30+2q32-28q33-16q35+16q36 -28q37-22q38+14q40+16q41+40q43-28q45+26q46+32q47-17q48-32q50-16q51-22q52-10q54 +32q55-34q56-8q57+14q58+45q60-4q61+38q62+8q63-34q66-8q67+38q68-22q70-56q71+2q72 -28q73-10q76+20q77+64q78-40q79-20q80+44q81+32q83+40q85+8q87-23q88-46q90-40q91 +16q92+16q93-16q95-46q96-32q98+26q100+O(q101) |
5 | 1-5q+5q2+10q3-15q4-6q5-5q6+25q7+15q8-20q9+9q10-45q11-5q12+25q13+20q14+10q15 +15q16+20q17-50q18-35q19-30q20+55q21-50q22+15q23+80q24+q25+50q26-35q27-45q28 -15q29+5q30-50q31-25q32-55q33+85q34+51q35+50q36+10q37-40q38+65q39+10q40-10q41 -115q42+50q43-115q44-100q45+85q46+80q47-30q48+5q49+20q50+45q51+70q52+65q53 +45q54-55q55-100q56-45q57+10q58-115q59+109q60-160q61+55q62-20q63-70q64+110q65 -20q66+105q67+185q68+70q69-130q70-85q71+65q72+60q73-50q74-q75-130q76+10q77 -55q78-165q79-110q80+165q81+15q82+55q83-30q84+160q85+45q86-60q87+90q88-5q89 +10q90+100q91+165q92-155q93+60q94-230q95-145q96-55q97-45q98+35q99+100q100+O(q101) |
6 | 1-6q+9q2+10q3-30q4+11q6+42q7-70q9+18q10-54q11+49q12+90q13-22q15-60q16-110q18 +81q20+180q21-78q22+130q24-198q25-182q27-30q28+90q29+121q30+84q31+210q34 -252q36-102q37-270q38+170q39-69q42+330q43-38q45+420q46-190q48-390q49-108q51 -300q55+99q56+442q57+210q58+418q60-294q61-510q64+378q65-540q66+138q67-230q69 -462q70+611q72+570q73+132q76+50q78-150q79+110q81-630q83-350q84-598q87+450q88 +361q90+660q91+162q92-550q93+420q94+378q97+650q99-798q100+O(q101) |
7 | 1-7q+14q2+7q3-49q4+21q5+35q6+41q7-49q8-133q9+98q10-21q11+126q12+112q13-176q14 -105q15-126q16+140q17-35q18+147q19+259q20+98q21-420q22-224q23+238q24-455q25 +273q26-14q27+322q28+406q29-35q30-7q31-637q32-196q33+245q34-181q35-574q36 +462q37+147q38+924q39+217q40-329q41-140q42-7q43-371q44-777q45+588q46-560q47 -196q48-489q49+1246q50+791q51+238q52+539q53-511q54-819q55+112q56+924q57 -1295q58-875q59+133q60-665q61-28q62+889q63-105q64+2093q65-770q66+1120q67 +336q68-1351q69+14q70-630q71+1400q72-483q73-1813q74-1820q75+749q76-560q77 +1071q78+1008q79+602q80+777q81+637q82-651q83+125q84+1162q85+126q86-1274q87 -378q88+7q89-980q90+154q91-2800q92-1421q93+1078q94+1841q95+315q96+980q97 +756q98+2653q99-3374q100+O(q101) |
8 | 1-8q+20q2-70q4+64q5+56q6-125q8-160q9+308q10+110q12-520q14+57q16+560q17 +182q20-512q21-880q22+1190q24-448q25+884q26-1400q30-1330q32+1000q33 +1820q34-646q36+1280q37-1331q40-2464q41+380q42+1120q44+2576q46-880q49 +1748q50-3850q52-3400q54+2703q56+4160q57-2500q58+3458q60-1150q64-456q65 -5236q66-4480q69+6032q70+6160q72-3220q74+4466q76-7378q80-1456q81-3920q82 +4096q85+2200q86+7040q89+812q90-4030q92+5600q94-4913q96-9520q97-10400q100 +O(q101) |
9 | 1-9q+27q2-12q3-90q4+135q5+54q6-99q7-189q8-85q9+657q10-162q11-135q12-171q13 -810q14+702q15+495q16+837q17-673q18-900q19+243q20-1053q21-297q22+1566q23 +2700q24-1764q25+81q26-1188q27-1377q28+270q29-2043q30+3321q31-756q32+3726q33 +3015q34-4563q35-3348q36+504q37-351q38-1350q39-468q40-891q41+7074q42+1611q43 +2700q44-2423q45-1512q46-3267q47-5265q48-1800q49+3510q50+2970q51-6741q52 +8910q53-1620q54+7227q55+7506q56-648q57-13923q58-9045q59+7884q60-5985q61 -2079q62-815q63+6930q64+1107q65-1485q66+12231q67+5049q68-8100q69+15075q70 -11205q71-4104q72-10719q73-18900q74+7371q75+5310q76+7587q77-756q78+6390q79 -11799q80+16632q81+4041q82+13500q83+1020q84-9117q85-297q86-23274q87-12078q88 +9180q89-4212q90-16236q91+5535q92+9855q93+29700q94-3780q95-2862q96-11034q97 +23463q98+13500q99-20322q100+O(q101) |
10 | 1-10q+35q2-30q3-105q4+238q5-260q7-165q8+140q9+1054q10-770q11-595q12-715q14 +2162q15+455q16-2380q18-1820q19+2401q20-680q21+1495q22+3080q23+1615q24 -6958q25-1925q26+5100q29-1442q30+8330q31-5355q32+1330q33-16790q35+8190q37 +8265q38+1918q40+8415q42-10230q43-7140q44-9362q45-7315q46+10010q47+14260q49 +14641q50+5320q51-21620q52+10150q53-15015q54+2925q56-24990q57-14105q58 +58765q60+2470q63+12155q64-20398q65-26455q66+17710q67-25025q68-24010q69 +28083q70-15950q71+24600q73+64078q75+9890q77-35815q78-37310q79-38398q80 +19530q81-3795q84-50370q85+69580q86-26640q87+44485q88+75670q89-45240q91 +12925q92-90482q95-61880q96+32045q98+59280q99-58562q100+O(q101) |
11 | 1-11q+44q2-55q3-110q4+374q5-143q6-462q7+55q8+495q9+1287q10-2069q11-902q12 +1210q13-275q14+3795q15-1507q16-2431q17-3575q18-385q19+8690q20-1661q21 +1143q22+1265q23-4290q24-12716q25+2299q26+11440q27+3905q28+8635q29-10472q30 +6105q31-20548q32-1540q33+8690q34-24904q35+29634q36+25003q37+8470q38 -23320q39-18183q40-4741q41+2420q42-19195q43+2200q44+18271q45+5643q46 +52382q47-14520q48+990q49-12287q50-39578q51-53823q52+21615q53+9460q54 +29580q55+43681q56-43901q57+34650q58+9185q59+105314q60-91036q61-108515q62 -9515q63+1760q64-17864q65-17842q66+142450q67-27885q68+27170q69+82566q70 -38984q71-42658q72+10890q73-49335q74+19580q75-125345q76-16257q77-30305q78 -47630q79+154308q80+154066q81+92037q82-36410q83-26125q84-178277q85 +182545q86-159610q87-20460q88+70400q89-227370q90-67155q91+37455q92 +173250q93+59785q94-55341q95+62733q96+281215q97+1430q98+94490q99 -306438q100+O(q101) |
12 | 1-12q+54q2-88q3-99q4+540q5-418q6-648q7+594q8+836q9+1056q10-4104q11-209q12 +4104q13-594q14+4256q15-6480q16-4752q17-298q18+5016q19+17226q20-12100q21 -5346q22-1296q23-9063q24-7128q25+19494q26+29160q27-10032q28-7668q29 -34738q30+8712q31-22572q32+21812q33+49248q34-46872q35+67562q36+2508q37 -47520q38-76912q39-25191q40+67716q41+32076q42+7128q43+29754q44+36784q45 -51072q46+45144q47-122398q48-53460q49+11286q50-27256q51+57024q52+122364q53 +99902q54+3576q55-29646q56-221616q57+41382q58-52272q59+130549q60-206712q61 -180036q62+336512q63+145200q64+100980q65-73568q66+221616q67-317142q68 -148324q69+15552q70-225720q71-32076q72+108756q73+196614q74+74360q75 -58806q76+229824q77+120878q78-233928q79+361152q80-111340q81-349920q82 -491832q83-196569q84-82764q85+707454q86+18392q87+92016q88+493668q89 -559450q90+416856q91-16092q92+320760q93-361152q94-724032q95+7106q96 +270864q97-530442q98+56168q99-261744q100+O(q101) |
13 | 1-13q+65q2-130q3-65q4+728q5-871q6-715q7+1560q8+845q9+78q10-6513q11+2730q12 +8605q13-4355q14+2483q15-13299q16-2275q17+11440q18+10010q19+19734q20-41834q21 -11375q22+12870q23-2730q24+14911q25+33201q26+25155q27-70070q28-36595q29 -28925q30+64389q31+13650q32+52780q33+72215q34-173693q35+87867q36-62920q37 -111865q38-25870q39+89908q40+284505q41-37895q42-88660q43-59995q44-57759q45 -172081q46+117390q47-121550q48+61490q49+301041q50-1261q51+167310q52-66950q53 -80080q54-319176q55-277680q56-224575q57+477620q58+239005q59+345371q60 -240422q61-363350q62+965575q63-283985q64-370369q65-669929q66+176605q67 -467740q68+44265q69+871637q70-15704q71+564135q72+173030q73+381875q74 -868595q75-668096q76+255905q77-345800q78-855270q79+993239q80+16198q81 -507780q82+254540q83+758745q84+1233895q85+975806q86-808730q87-1524900q88 -152880q89-2178202q90+1332566q91-400335q92+649480q93+56745q94-1204515q95 +2694510q96+973115q97-620620q98+284375q99-123734q100+O(q101) |
14 | 1-14q+77q2-182q3+924q5-1547q6-506q7+3003q8-1729q10-8372q11+9177q12+13090q13 -15625q14-17017q16+10556q17+30107q18+7084q20-89206q21+11571q22+69160q23 +27132q25-19096q27-153502q28+93093q30+165242q31-38962q33-420838q35 +257439q36-76153q38+218750q39+168245q40+397320q41-638066q42-399126q43 +67158q45+92092q46+530348q47+424879q50-659736q51-96019q52-629706q53 +56446q56+839762q57+1248884q58-651651q60-1262884q61-1272271q62+2172742q63 -1203125q64-566370q65+1525510q67+893893q68+1771561q70-1979978q71-467544q72 -1599598q73-2244242q75+245973q76+3796114q77+2678571q80-3114111q82+782782q85 -2185183q86-3062864q87-1774409q88+2843750q89+1467389q90+7082714q91-701624q93 -6868862q95+5891732q96-4244240q97-4570773q98+O(q101) |
15 | 1-15q+90q2-245q3+105q4+1107q5-2485q6+195q7+4860q8-2420q9-3990q10-8190q11 +19695q12+13755q13-38475q14+3990q15-9750q16+34020q17+43015q18-46605q19 -13860q20-127385q21+106485q22+165240q23-79275q24-16380q25-92340q26 -35840q27-151995q28+188550q29+315783q30+90090q31-271215q32-307485q33 +20475q34-505440q35+915385q36+209340q37-284130q38+337645q39-294225q40 +269325q41-1707970q42-70305q43+1297620q44+574210q45+492765q46+251370q47 -847245q48-1102725q49+438129q50-1416190q51+641445q52+1537330q54+1239420q55 -800370q56+1403815q57-472080q58-2750895q59-2707950q60-761490q61+952560q62 +7162255q63-1869450q64-1047150q65+1169350q66+728805q67+500175q68-5564055q69 +1575990q70-5375160q71+939590q72+1736280q73+4629870q74+151789q75+2775045q76 +8922960q77-9469990q78-4736745q79-408240q80-2820545q81-7843095q82+4410630q83 +7312455q84+4813590q85-2678940q86-1306095q87+4328205q88+4383720q89+2850575q90 +650415q91-16312140q92-13250360q93+3613365q94-10234350q95+25950965q96 -2986830q97-126360q98+14627375q99-1348440q100+O(q101) |
16 | 1-16q+104q2-320q3+260q4+1248q5-3712q6+1664q7+6890q8-7280q9-5568q10-4160q11 +33176q12+4640q13-74240q14+29824q15+14035q16+54288q17+27040q18-142720q19 +1508q20-110240q21+289536q22+222720q23-380770q24-83200q25-123904q26 +142912q27+7640q28+408000q29+386048q30-530816q31-755943q32-294320q33 +716560q34-194688q35+1843200q36-250432q37-1688960q38+324480q39-988858q40 +1025440q41-2283008q42+1963520q43+3857360q44-1118240q45-965120q46-2204800q47 -2004730q48-976720q49+3450304q50-24128q51+2699684q52+432640q53+1076480q54 -451456q55-7188480q56+2619760q57-2478080q58-3020160q59+1791400q60+6092320q61 +6919168q62+8444800q63-12957490q64-10023792q65+1459640q66-1892800q67 +5073260q68-10616320q69+12594816q70-122240q71+6593834q72+8598720q73 -1447680q74-8932928q75-9584640q76+9821760q77-33111040q78+2245760q79 +17376829q80+12095088q81+156832q82+14439360q83+19536140q84-16841344q85 -25575680q86-14283776q87+8625760q88-5793840q89+9664512q90-4491200q91 -24466864q92+11228800q93+51671040q94+1206400q95+41932800q96-36465904q97 -39600080q98+11464960q99-51210172q100+O(q101) |
17 | 1-17q+119q2-408q3+476q4+1309q5-5236q6+4233q7+8602q8-15470q9-4250q10 +5236q11+45815q12-21182q13-117776q14+101065q15+46767q16+36685q17 -36771q18-267036q19+143514q20-18241q21+486285q22+81753q23-1007250q24 +104006q25+165767q26+579292q27+78829q28+187510q29+60214q30-1706885q31 -616539q32+956879q33+2210985q34-450109q35+1609730q36-2449615q37 -4158149q38+2521015q39-86275q40+3856314q41-3279895q42+3835982q43 +4922435q44-9624346q45-2911454q46-2670955q47+2759372q48+4788186q49 +8763296q50-1458226q51-2635578q52-4968726q53-3810499q54-1407056q55 -12497091q56+18737893q57+2339897q58-1052504q59+9495486q60+3509548q61 +377230q62-11630278q63-34437716q64-8162924q65+30006496q66+13662390q67 +23888060q68-24836966q69+21011609q70-6870006q71-18795455q72+5104029q73 -33117700q74-8367604q75-1641486q76+52566397q77-39513678q78+44706396q79 +54200539q80-12925899q81-40685981q82-37586745q83+22511570q84-83964529q85 -22329993q86+45760175q87+85152354q88+15299949q89+35615510q90-20577854q91 -78717480q92+43606717q93+58079344q94-76352661q95-41144488q96-98414190q97 -37231054q98+138897276q99-28365673q100+O(q101) |
18 | 1-18q+135q2-510q3+765q4+1242q5-7038q6+8280q7+9180q8-27710q9+3519q10 +20196q11+50370q12-68850q13-153765q14+244782q15+52785q16-71010q17 -130525q18-343620q19+517293q20+54978q21+498780q22-390150q23-1835865q24 +1161270q25+896751q26+793730q27-633420q28-906660q29-75582q30-2589984q31 +1523745q32+3589380q33+2472615q34-3740850q35-767039q36-4649670q37 -4222800q38+11166210q39+1718937q40+4728294q41-10403235q42+2349450q43 +5331285q44-23826622q45+6799950q46+7601040q47+14132100q48+7375230q49 -989604q50-16889958q51-19556595q52-1794690q53+6516610q54+16045416q55 -10484343q56+48988800q57-10299960q58-31037580q59+6486723q60-21198150q61 -924885q62-25688700q63-14287140q64+52029486q65+86795778q66+45900q67 -17620875q68-112599720q69+9017955q70+1360476q71-46670270q72+78420150q73 -34415820q74+65991042q75+38393973q76+75746610q77-124838820q78+7422030q79 +38533050q80-156118718q81-71136585q82-26920350q83+236345730q84-89959716q85 +90024723q86+195022980q87+36215100q88-156734730q89-153057119q90-131160492q91 -200991780q92+265786500q93+162542475q94-101009376q95-47854881q96+62559540q97 +175246200q98+277603200q99-229438800q100+O(q101) |
19 | 1-19q+152q2-627q3+1140q4+988q5-9063q6+14212q7+7410q8-44270q9+22781q10 +38114q11+36176q12-137256q13-154850q14+480605q15-46493q16-316065q17 -153406q18-254525q19+1156948q20-184927q21+88483q22-1051042q23-2381650q24 +3838874q25+1417039q26-542146q27-2649911q28-2171510q29+2131306q30 -2282489q31+5694509q32+5022973q33-2849050q34-10735551q35-1364789q36 -88825q37+1790369q38+24936550q39-6189326q40-6533150q41-25397471q42 +6233254q43+19679725q44-38263549q45+39975430q46+19318117q47+5441714q48 -16667750q49-38728042q50-21361890q51-14130091q52+53481675q53+43468390q54 +22319015q55-50330164q56+50345744q57-75352822q58-94570220q59+68312543q60 -8312291q61+71890148q62-20446584q63+30514950q64+103261770q65+16151577q66 -151065846q67-145680429q68-157437800q69+182701226q70+206241979q71-51212942q72 +216299534q73-166282300q74+38220590q75-66544764q76-101781195q77-247633897q78 +20258940q79+282976937q80-200744519q81+176447129q82+143955989q83+557438530q84 -503453792q85-174385629q86+185045427q87-482281636q88-306034900q89-123226457q90 +430280213q91+140634846q92+1007804232q93+159587175q94-714427549q95-484438364q96 +44967908q97+272676277q98-226384050q99-671337716q100+O(q101) |
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Last Update: 2005.06.12 |
H.Nakao |