A294506 E.g.f.: 1/Product_{k>0} (1-x^(2*k-1)/(2*k-1)).

1, 1, 2, 8, 32, 184, 1184, 9008, 74752, 726528, 7583232, 87931392, 1092516864, 14863589376, 215094226944, 3358032635904, 55181218873344, 970561417248768, 17945595514847232, 351221170194874368, 7186120683011702784, 155103171658691641344

Offset: 0

Author

Seiichi Manyama, Nov 01 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..449
• D. H. Lehmer, On reciprocally weighted partitions, Acta Arithmetica XXI (1972), 379-388 (Theorem 5).

Crossrefs

Cf. A007838, A007841, A087639, A088994, A309319.

Programs

Mathematica

nmax = 30; CoefficientList[Series[1/Product[(1-x^(2*k-1)/(2*k-1)), {k, 1, Floor[nmax/2] + 1}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Nov 02 2017 *)

Formula

a(n) ~ 2*exp(-gamma/2) * sqrt(2*n) * n! / Pi, where gamma is the Euler-Mascheroni constant A001620 [Lehmer, 1972]. - Vaclav Kotesovec, Jul 23 2019