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'_2 = (E_2^2-E_4)/12.
a(n) = 24*A064987(n).
G.f.: 24*x*f'(x), where f(x) = Sum_{k>=1} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Aug 31 2017
EXAMPLE
G.f. = 24*q + 144*q^2 + 288*q^3 + 672*q^4 + 720*q^5 + ...
MAPLE
with(numtheory); E:=proc(k) series(1-(2*k/bernoulli(k))*add( sigma[k-1](n)*q^n, n=1..60), q, 61); end; -diff(E(2), q);
MATHEMATICA
terms = 41;
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}];
-(E2[x]^2 - E4[x])/12 + 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