OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Vaclav Kotesovec)
N. J. A. Sloane, Transforms
FORMULA
Euler transform of sequence [0, 3, 4, 5, 6, ...].
G.f.: Product_{k=2..infinity} 1/(1-x^k)^(k+1).
From Vaclav Kotesovec, Mar 09 2015: (Start)
a(n) ~ 2^(1/36) * Zeta(3)^(37/36) * exp(1/12 - Pi^4/(432*Zeta(3)) + Pi^2 * n^(1/3) / (3*2^(4/3)*Zeta(3)^(1/3)) + 3*Zeta(3)^(1/3) * n^(2/3) / 2^(2/3)) / (A * 3^(1/2) * Pi * n^(55/36)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... .
a(n) ~ (2*Zeta(3))^(2/3) * A005380(n) / n^(2/3).
(End)
MATHEMATICA
nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(k+1), {k, 2, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 04 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 23 2001
EXTENSIONS
Edited by Christian G. Bower, Jan 08 2004
STATUS
approved