OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ Zeta(3)^(7/36) * 2^(25/36) * exp(3 * Zeta(3)^(1/3) * (n/2)^(2/3) + 1/12) / (A * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jul 20 2019
MAPLE
G:= (1+x)/mul((1-x^k)^k, k=1..100):
S:= series(G, x, 101):
seq(coeff(S, x, j), j=0..100); # Robert Israel, Dec 01 2020
MATHEMATICA
nmax = 38; CoefficientList[Series[(1 + x) Product[1/(1 - x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[DivisorSigma[2, k] a[n - k], {k, 1, n}]/n; Table[a[n] + a[n - 1], {n, 0, 38}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 20 2019
STATUS
approved