A293716 E.g.f.: exp(x + 2*x^2 + 3*x^3).

1, 1, 5, 31, 145, 1181, 9661, 77155, 794081, 8132185, 86715541, 1055208551, 12921555505, 166589628661, 2320023320525, 32814550442731, 486870347843521, 7598251948512305, 121035455085677221, 2008950533339620015, 34595064617371963601, 609252363677557660621

Offset: 0

Author

Seiichi Manyama, Oct 15 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..533

Crossrefs

Column k=3 of A293718.

Programs

Mathematica

CoefficientList[Series[E^(x+2*x^2+3*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+2*x^2+3*x^3)))

Formula

a(n) ~ 3^(2*n/3 - 1/2) * n^(2*n/3) * exp(-76/729 + 19*3^(1/3)*n^(1/3)/81 + 2*3^(2/3)*n^(2/3)/9 - 2*n/3). - Vaclav Kotesovec, Oct 15 2017