OFFSET
0,2
COMMENTS
Convergent of columns of A091355.
LINKS
Joerg Arndt and Vaclav Kotesovec, Table of n, a(n) for n = 0..5000 (first 500 terms from Joerg Arndt)
N. J. A. Sloane, Transforms
FORMULA
Euler transform of 2, 2, 3, 4, 5, 6, 7, 8, 9, ...
G.f.: 1/( (1-x) * prod(n>=1, (1-x^n)^n ) ). [Joerg Arndt, Mar 15 2014]
From Vaclav Kotesovec, Aug 16 2015: (Start)
a(n) = Sum_{k=0..n} A000219(k).
a(n) ~ (n/(2*Zeta(3)))^(1/3) * A000219(n).
a(n) ~ exp(1/12 + 3 * Zeta(3)^(1/3) * n^(2/3) / 2^(2/3)) / (A * 2^(23/36) * sqrt(3*Pi) * Zeta(3)^(5/36) * n^(13/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
(End)
G.f.: exp(Sum_{k>=1} (sigma_2(k) + 1)*x^k/k). - Ilya Gutkovskiy, Aug 21 2018
MATHEMATICA
CoefficientList[Series[1/(1-x)*Product[1/(1-x^k)^k, {k, 1, 50}], {x, 0, 50}], x] (* Vaclav Kotesovec, Aug 16 2015 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec( 1/((1-x)*prod(n=1, N, (1-x^n)^n )) ) \\ Joerg Arndt, Mar 15 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 02 2004
STATUS
approved