A358741 Expansion of Sum_{k>=0} k! * ( k * x/(1 - x) )^k.

1, 1, 9, 179, 6655, 400581, 35530421, 4357960999, 706230728379, 146116931998025, 37577989723572001, 11758017370126904091, 4398121660346674034039, 1938019214715102033590029, 993580299268226843514372045, 586357970017371399763899232271

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = Sum_{k=1..n} k! * k^k * binomial(n-1,k-1) for n > 0.

a(n) ~ n! * n^n. - Vaclav Kotesovec, Feb 18 2023

Mathematica

nmax = 20; CoefficientList[1 + Series[Sum[k! * (k * x/(1 - x))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 18 2023 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*(k*x/(1-x))^k))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, k!*k^k*binomial(n-1, k-1)));

Crossrefs

Cf. A358738, A358740.

Cf. A355494.

Sequence in context: A009009 A220267 A304402 * A034221 A034240 A163132

Adjacent sequences: A358738 A358739 A358740 * A358742 A358743 A358744

Keyword

nonn

Author

Seiichi Manyama, Nov 29 2022

Status

approved