A258344 Expansion of Product_{k>=1} (1+x^k)^(k*(k-1)).

1, 0, 2, 6, 13, 32, 69, 160, 344, 760, 1601, 3384, 7022, 14434, 29361, 59140, 118089, 233754, 459293, 895382, 1733904, 3334914, 6374654, 12111632, 22881777, 42993244, 80362496, 149464404, 276657082, 509740278, 935046158, 1707916988, 3106810873, 5629121054

Offset

0,3

Links

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

Formula

a(n) ~ 7^(1/8) / (2^(43/24) * 15^(1/8) * n^(5/8)) * exp(-2025*Zeta(3)^3 / (49*Pi^8) - 135*(15/14)^(1/4) * Zeta(3)^2 / (14*Pi^5) * n^(1/4) - 3*sqrt(15/14) * Zeta(3) / Pi^2 * sqrt(n) + 2*(14/15)^(1/4)*Pi/3 * n^(3/4)), where Zeta(3) = A002117.

Mathematica

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

Crossrefs

Cf. A027998, A028377, A027999, A258341, A258342, A258343, A258345, A258346, A258348.

Sequence in context: A018013 A263899 A062424 * A099232 A280758 A053562

Adjacent sequences: A258341 A258342 A258343 * A258345 A258346 A258347

Keyword

nonn

Author

Vaclav Kotesovec, May 27 2015

Status

approved