A293487 E.g.f.: Product_{m>0} (1 + x^(2*m-1)).

1, 1, 0, 6, 24, 120, 720, 5040, 80640, 725760, 7257600, 79833600, 1437004800, 18681062400, 261534873600, 5230697472000, 104613949440000, 1778437140480000, 32011868528640000, 729870602452992000, 17030314057236480000, 408727537373675520000, 8992005822220861440000

Offset: 0

Author

Seiichi Manyama, Oct 10 2017

Keywords

• nonn

Crossrefs

Column k=1 of A293486.

Cf. A000700, A293300.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[1 + x^(2*k-1), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 15 2017 *)

PARI

N=66; x='x+O('x^N); Vec(serlaplace(prod(m=1, N, 1+x^(2*m-1))))

Formula

a(n) = n! * A000700(n).

a(n) ~ sqrt(Pi) * exp(Pi*sqrt(n/6) - n) * n^(n - 1/4) / (2^(5/4) * 3^(1/4)). - Vaclav Kotesovec, Oct 15 2017