A293494 E.g.f.: exp(x^2/(1 - x^3)).

1, 0, 2, 0, 12, 120, 120, 5040, 42000, 181440, 5473440, 46569600, 479666880, 12713500800, 123519876480, 2190354566400, 54922842374400, 652587628492800, 16192687807296000, 400439258111692800, 5994400896144460800, 182793304684134144000, 4590673238662192281600

Offset: 0

Author

Seiichi Manyama, Oct 10 2017

Keywords

• nonn

Crossrefs

Cf. A293493.

Programs

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(x^2/(1-x^3))))

PARI

N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(3*k-1)))))

Formula

E.g.f.: Product_{k>0} exp(x^(3*k-1)).

a(n) ~ exp(2*sqrt(3*n)/3 - n - 1/6) * n^(n-1/4) / (sqrt(2) * 3^(1/4)). - Vaclav Kotesovec, Oct 10 2017