A293721 E.g.f.: exp(x + 4*x^2 + 9*x^3).

1, 1, 9, 79, 457, 5901, 66841, 720259, 11155089, 158315257, 2361665161, 42133751991, 720156599449, 13181971424389, 265545621153177, 5280775950377131, 111888028465044001, 2508562975185903729, 56507353426001537929, 1342159313030965211167

Offset: 0

Author

Seiichi Manyama, Oct 15 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..497

Crossrefs

Column k=3 of A293724.

Programs

Mathematica

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

PARI

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

Formula

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