A326855 E.g.f.: Product_{k>=1} (1 + x^(4*k-1) / (4*k-1)).

1, 0, 0, 2, 0, 0, 0, 720, 0, 0, 172800, 3628800, 0, 0, 2641766400, 87178291200, 0, 0, 225422681702400, 6402373705728000, 0, 221172909834240000, 30424079849619456000, 1124000727777607680000, 0, 49241936645495193600000, 11321261082950211993600000

Offset: 0

Author

Vaclav Kotesovec, Jul 27 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..440
• Vaclav Kotesovec, Graph - the asymptotic ratio (40000 terms)

Crossrefs

Cf. A007838, A088994, A326779, A326856, A326857.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[(1+x^(4*k-1)/(4*k-1)), {k, 1, Floor[nmax/4]+1}], {x, 0, nmax}], x] * Range[0, nmax]!

Formula

a(n) ~ Pi * n! / (exp(gamma/4) * Gamma(1/4)^2 * n^(3/4)), where gamma is the Euler-Mascheroni constant A001620 and Gamma() is the Gamma function.