A306624 Expansion of e.g.f. exp(Sum_{k=1..9} x^k).

1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553, 55312291, 744239541, 10793656633, 167689950013, 2775839905203, 48726598412521, 903159189729121, 17607070923233553, 359702718305842243, 7673827033741108573, 171586828999546057641, 3999150173195168500741

Offset: 0

Author

Seiichi Manyama, Mar 01 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..465

Crossrefs

Column 9 of A293669.

Programs

Mathematica

m=21; CoefficientList[Series[Exp[Sum[x^k, {k,1,9}]], {x, 0, m}], x] * Range[0,m]! (* Amiram Eldar, Mar 01 2019 *)

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, 9, x^k))))

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..min(9,n)} k*a(n-k)/(n-k)! for n > 0.