A326862 E.g.f.: Product_{k>=1} (1 + x^(4*k-1)/(4*k-1)) / (1 - x^(4*k-1)/(4*k-1)).

1, 0, 0, 4, 0, 0, 160, 1440, 0, 26880, 691200, 7257600, 11827200, 395366400, 14125363200, 185119334400, 442810368000, 24049778688000, 919255538073600, 13662913904640000, 54833495408640000, 3627817738960896000, 142917996623560704000, 2442221696292618240000

Offset: 0

Author

Vaclav Kotesovec, Jul 27 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A326855, A326779.

Cf. A305199, A326859, A326860, A326863.

Programs

Mathematica

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

Formula

a(n) ~ exp(-gamma/2) * n! / (2*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620.