A091360 Partial sums of A000219.

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

Cf. A000219, A002117, A074962.

Sequence in context: A091358 A091359 A059776 * A300277 A294378 A090764

Adjacent sequences: A091357 A091358 A091359 * A091361 A091362 A091363

Keyword

nonn

Author

Christian G. Bower, Jan 02 2004

Status

approved