A266942 Expansion of Product_{k>=1} ((1 + k*x^k) / (1 - k*x^k))^k.

1, 2, 10, 36, 118, 376, 1156, 3392, 9734, 27230, 74256, 198724, 522292, 1348968, 3432824, 8613856, 21330374, 52190692, 126262774, 302222388, 716247128, 1681575344, 3912919956, 9028823856, 20667406276, 46949343786, 105881451120, 237135574392, 527580701456

Offset: 0

Author

Vaclav Kotesovec, Jan 06 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A006906, A022629, A265758, A266891, A266941.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[((1+k*x^k)/(1-k*x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

From Vaclav Kotesovec, Jan 08 2016: (Start)

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

c = 1122422673446372185062691708933615715850.583956830118389527... if mod(n,3)=0

c = 1122422673446372185062691708933615715849.484130848291097773... if mod(n,3)=1

c = 1122422673446372185062691708933615715849.782119252925454917... if mod(n,3)=2

(End)