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

0,3

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Column 9 of A293669.

Sequence in context: A193932 A193933 A306623 * A293125 A000262 A367751

Adjacent sequences: A306621 A306622 A306623 * A306625 A306626 A306627

Keyword

nonn

Author

Seiichi Manyama, Mar 01 2019

Status

approved