A294780 Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(k*(k-1)/2).

1, 0, 2, 6, 14, 32, 74, 166, 370, 810, 1736, 3682, 7718, 15976, 32754, 66508, 133794, 266948, 528424, 1038178, 2025456, 3925360, 7559298, 14470162, 27540598, 52130440, 98159832, 183905636, 342896254, 636384748, 1175823512, 2163221030, 3963353706, 7232529308

Offset

0,3

Comments

Convolution of A027999 and A258349.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

Formula

a(n) ~ exp(2*Pi * n^(3/4) / 3 - 7*Zeta(3) * sqrt(n) / (2*Pi^2) - 49*Zeta(3)^2 * n^(1/4) / (4*Pi^5) - 22411 * Zeta(3)^3 / (392*Pi^8) - Zeta(3) / (8*Pi^2) - 1/24) * sqrt(A) / (2^(23/12) * Pi^(1/24) * n^(59/96)), where A is the Glaisher-Kinkelin constant A074962.

Mathematica

nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(k*(k-1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A027999, A156616, A206622, A258349, A294779.

Sequence in context: A065495 A131352 A232230 * A051485 A077999 A110524

Adjacent sequences: A294777 A294778 A294779 * A294781 A294782 A294783

Keyword

nonn

Author

Vaclav Kotesovec, Nov 08 2017

Status

approved