A294778 Expansion of Product_{k>=1} 1/(1 - x^(2*k-1))^(k*(k-1)/2).

1, 0, 0, 1, 0, 3, 1, 6, 3, 11, 12, 18, 29, 33, 69, 67, 138, 141, 275, 306, 516, 656, 972, 1353, 1828, 2712, 3477, 5280, 6654, 10038, 12756, 18789, 24369, 34796, 46167, 63990, 86629, 117189, 160698, 213984, 295092, 389517, 536683, 706590, 968289, 1276310

Offset

0,6

Links

Table of n, a(n) for n=0..45.

Formula

a(n) ~ exp(2*Pi * n^(3/4) / (3^(5/4) * 5^(1/4)) - 5^(1/4) * Pi * n^(1/4) / (16*3^(3/4)) + 3*Zeta(3) / (32*Pi^2)) / (2^(31/16) * 15^(1/8) * n^(5/8)).

Mathematica

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

Crossrefs

Cf. A023871, A035528, A258349, A294750.

Sequence in context: A121443 A008795 A165188 * A132180 A207630 A368376

Adjacent sequences: A294775 A294776 A294777 * A294779 A294780 A294781

Keyword

nonn

Author

Vaclav Kotesovec, Nov 08 2017

Status

approved