A289639
Coefficients in expansion of -q*E'_10/E_10 where E_10 is the Eisenstein Series (A013974).
Original entry on oeis.org
264, 340560, 141251616, 85062410400, 43377095394864, 23729517350865216, 12591243615814264896, 6769208775901467246912, 3618692733697667332476264, 1939201752717876551124987360, 1038098212042387655796115897440
Offset: 1
-
nmax = 20; Rest[CoefficientList[Series[264*x*Sum[k*DivisorSigma[9, k]*x^(k-1), {k, 1, nmax}]/(1 - 264*Sum[DivisorSigma[9, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 09 2017 *)
A289640
Coefficients in expansion of -q*E'_14/E_14 where E_14 is the Eisenstein Series (A058550).
Original entry on oeis.org
24, 393840, 128962656, 87898218720, 42722691563664, 23880530579622336, 12556395110261366976, 6777250576938845733312, 3616836970791932655993144, 1939629997080836352904793760, 1037999388408269242271021494560
Offset: 1
-
nmax = 20; Rest[CoefficientList[Series[24*x*Sum[k*DivisorSigma[13, k]*x^(k-1), {k, 1, nmax}]/(1 - 24*Sum[DivisorSigma[13, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 09 2017 *)
A289637
Coefficients in expansion of -q*E'_6/E_6 where E_6 is the Eisenstein Series (A013973).
Original entry on oeis.org
504, 287280, 153540576, 82226602080, 44031499226064, 23578504122108096, 12626092121367162816, 6761166974864088760512, 3620548496603402008959384, 1938773508354916749345180960, 1038197035676506069321210300320
Offset: 1
-
nmax = 20; Rest[CoefficientList[Series[504*x*Sum[k*DivisorSigma[5, k]*x^(k-1), {k, 1, nmax}]/(1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 09 2017 *)
A289141
Table of expansion of j_n in powers of j (A000521).
Original entry on oeis.org
1, -744, 1, 159768, -1488, 1, -36866976, 1069956, -2232, 1, 8507424792, -561444608, 2533680, -2976, 1, -1963211493744, 246683410950, -2028551200, 4550940, -3720, 1, 453039686271072, -96687754014528, 1304194222980, -4850017536, 7121736, -4464, 1
Offset: 0
The table a(n,m) starts:
n\m 0 1 2 3 4
0: 1
1: -744, 1
2: 159768, -1488, 1
3: -36866976, 1069956, -2232, 1
4: 8507424792, -561444608, 2533680, -2976, 1
Original entry on oeis.org
42, 11949, 4265002, 1713048225, 733858320426, 327479221781677, 150310620492466218, 70428822653977730817, 33523597190772239402026, 16156445902957272648713901, 7865129058155349010009168938, 3860735065245250133098748713633
Offset: 1
A294183
Coefficients in expansion of E_6/E_8.
Original entry on oeis.org
1, -984, 393768, -129252576, 38684099112, -10970838627984, 3003345011096352, -801909012374388672, 210169391033048138280, -54295810529811041175672, 13867098270790394508774768, -3508693915623201191415922848
Offset: 0
-
terms = 12;
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];
E6[x]/E8[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)