A258386 Expansion of Product_{k>=1} 1/(1-x^k)^(k+(-1)^k).

1, 0, 3, 2, 11, 10, 35, 40, 107, 138, 310, 432, 871, 1262, 2355, 3504, 6186, 9318, 15799, 23934, 39351, 59672, 95772, 144970, 228258, 344244, 533552, 800952, 1225164, 1829530, 2767227, 4109504, 6155310, 9089834, 13497964, 19822252, 29208812, 42660456

Offset: 0

Author

Vaclav Kotesovec, May 28 2015

Keywords

• nonn

Links

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

Crossrefs

Cf. A000219, A106507.

Programs

Mathematica

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

Formula

a(n) ~ (2*Zeta(3))^(13/36) / (sqrt(3) * Pi * n^(31/36)) * exp(Zeta'(-1) + 3*Zeta(3)^(1/3) * (n/2)^(2/3)), where Zeta(3) = A002117, Zeta'(-1) = A084448 = 1/12 - log(A074962). - Vaclav Kotesovec, May 28 2015