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A091360
Partial sums of A000219.
15
1, 2, 5, 11, 24, 48, 96, 182, 342, 624, 1124, 1983, 3462, 5947, 10114, 16993, 28290, 46624, 76225, 123555, 198833, 317627, 504102, 794885, 1246079, 1942112, 3010857, 4643515, 7126749, 10886361, 16555324, 25067633, 37801062, 56776035, 84951990, 126643036, 188127997, 278507781, 410949776, 604437277, 886284200, 1295668181
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