A293526 E.g.f.: exp(x^3/(1 - x^4)).

1, 0, 0, 6, 0, 0, 360, 5040, 0, 60480, 3628800, 39916800, 19958400, 3113510400, 130767436800, 1318571654400, 3487131648000, 355687428096000, 12813639597158400, 126713646259200000, 1013709170073600000, 85161707377883136000, 2819368492175499264000

Offset: 0

Author

Seiichi Manyama, Oct 11 2017

Keywords

• nonn

Crossrefs

E.g.f.: Product_{k>0} exp(x^(m*k-1)): A088009 (m=2), A293494 (m=3), this sequence (m=4).

Cf. A293507.

Programs

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(x^3/(1-x^4))))

PARI

N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(4*k-1)))))

Formula

E.g.f.: Product_{k>0} exp(x^(4*k-1)).

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