A306623 Expansion of e.g.f. exp(Sum_{k=1..8} x^k).

1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4233673, 51683491, 684364341, 9755819833, 148749428413, 2411870539443, 41369113878121, 746931540551521, 14128241450715153, 281805883597349443, 5880463849670410333, 128050607992266620841, 2903233047048502113541

Offset: 0

Author

Seiichi Manyama, Mar 01 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..469

Crossrefs

Column 8 of A293669.

Programs

Mathematica

m=21; CoefficientList[Series[Exp[Sum[x^k, {k,1,8}]], {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, 8, x^k))))

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..min(8,n)} k*a(n-k)/(n-k)! for n > 0.