%I #12 Oct 16 2017 12:39:08

%S 1,1,9,79,457,5901,66841,720259,11155089,158315257,2361665161,

%T 42133751991,720156599449,13181971424389,265545621153177,

%U 5280775950377131,111888028465044001,2508562975185903729,56507353426001537929,1342159313030965211167

%N E.g.f.: exp(x + 4*x^2 + 9*x^3).

%H Seiichi Manyama, <a href="/A293721/b293721.txt">Table of n, a(n) for n = 0..497</a>

%F a(n) ~ 3^(n - 1/2) * n^(2*n/3) * exp(-392/6561 - 2*n/3 + 49*n^(1/3)/243 + 4*n^(2/3)/9). - _Vaclav Kotesovec_, Oct 15 2017

%t CoefficientList[Series[E^(x + 4*x^2 + 9*x^3), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 15 2017 *)

%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x+4*x^2+9*x^3)))

%Y Column k=3 of A293724.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 15 2017