A151954 Expansion of Product_{k>0} (1-k^2*x^k)^(-1/k).

1, 1, 3, 6, 16, 27, 79, 126, 331, 632, 1436, 2509, 6800, 11218, 26044, 51958, 114941, 205183, 502228, 875545, 2027193, 3963938, 8389190, 15504996, 37555290, 66502859, 145809046, 292860564, 621638120, 1156065731, 2701045579

Offset: 0

Author

Franklin T. Adams-Watters, Jul 03 2009

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3149

Crossrefs

Cf. A028342, A073705, A077335.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1-k^2*x^k)^(-1/k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 05 2017 *)

Formula

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} A073705(k)*a(n-k) for n > 0. - Seiichi Manyama, Nov 05 2017

From Vaclav Kotesovec, Nov 05 2017: (Start)

a(n) ~ c * 3^(2*n/3) / n^(2/3), where

c = 4.674336739118905298732313884863019... if mod(n,3)=0

c = 4.299861572054701010776554223312792... if mod(n,3)=1

c = 4.239106098573472870377481583112857... if mod(n,3)=2

(End)