A294777 Expansion of Product_{k>=1} (1 + x^(2*k-1))^(k*(k-1)/2).

1, 0, 0, 1, 0, 3, 0, 6, 3, 10, 9, 15, 28, 24, 60, 47, 126, 99, 227, 225, 414, 498, 717, 1044, 1301, 2082, 2364, 3984, 4482, 7353, 8513, 13287, 16317, 23698, 30789, 42081, 57499, 74763, 105276, 133273, 190155, 238122, 338291, 425775, 596142, 759651, 1041498

Offset: 0

Author

Vaclav Kotesovec, Nov 08 2017

Keywords

• nonn

Crossrefs

Cf. A027998, A027999, A263140, A294749.

Programs

Mathematica

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

Formula

a(n) ~ exp(Pi*14^(1/4) * n^(3/4) / (3^(5/4) * 5^(1/4)) - Pi*5^(1/4) * n^(1/4) / (2^(17/4) * 3^(3/4) * 7^(1/4))) * 7^(1/8) / (2^(19/8) * 15^(1/8) * n^(5/8)).