A282020 Coefficients in q-expansion of (E_2^3 - E_2*E_4)/288, where E_2 and E_4 are the Eisenstein series shown in A006352 and A004009, respectively.

0, -1, 18, 204, 788, 2250, 4968, 9688, 17640, 27747, 45900, 64548, 98448, 128674, 188496, 232200, 326864, 386478, 537354, 608380, 819000, 926688, 1214136, 1323144, 1758240, 1852625, 2401308, 2584440, 3252256, 3385170, 4374000, 4433248, 5604768, 5840208, 7143876, 7232400, 9239364, 9058858

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = (A282018(n) - A282019(n))/288. - Seiichi Manyama, Feb 06 2017

Maple

with(numtheory); M:=100;
E := proc(k) local n, t1; global M;
t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..M+1);
series(t1, q, M+1); end;
e2:=E(2); e4:=E(4); e6:=E(6);
series((e2^3-e2*e4)/288, q, M+1);
seriestolist(%);

Mathematica

terms = 38;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms + 1}];
(E2[x]^3 - E2[x]*E4[x])/288 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)

Crossrefs

Cf. A282018 (E_2^3), A282019 (E_2*E_4).

Sequence in context: A250558 A282833 A181400 * A277763 A028025 A109126

Adjacent sequences: A282017 A282018 A282019 * A282021 A282022 A282023

Keyword

sign

Author

N. J. A. Sloane, Feb 06 2017

Status

approved