OFFSET
1,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998.
Eric Weisstein's World of Mathematics, Eisenstein Series
FORMULA
q*E'_4 = (E_2*E_4-E_6)/3.
G.f.: 240*x*f'(x), where f(x) = Sum_{k>=1} k^3*x^k/(1 - x^k). - Ilya Gutkovskiy, Aug 31 2017
Sum_{k=1..n} a(k) ~ 8 * Pi^4 * n^5 / 15. - Vaclav Kotesovec, May 09 2022
EXAMPLE
G.f. = 240*q + 4320*q^2 + 20160*q^3 + 70080*q^4 + 151200*q^5 + ...
MATHEMATICA
terms = 28;
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}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
(E2[x]*E4[x] - E6[x])/3 + O[x]^terms // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Feb 23 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 28 2009
STATUS
approved