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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)