A293494 - OEIS

%I #12 Oct 10 2017 19:23:33

%S 1,0,2,0,12,120,120,5040,42000,181440,5473440,46569600,479666880,

%T 12713500800,123519876480,2190354566400,54922842374400,

%U 652587628492800,16192687807296000,400439258111692800,5994400896144460800,182793304684134144000,4590673238662192281600

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

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

%F 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

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

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

%Y Cf. A293493.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 10 2017