A355494 Expansion of Sum_{k>=0} (k * x/(1 - x))^k.

1, 1, 5, 36, 350, 4328, 65132, 1155904, 23640724, 547544032, 14166236708, 404944248104, 12674392793900, 431104742439088, 15834117059443828, 624575921756875960, 26332801242942780668, 1181750740315156943936, 56244454481507648435012

Offset

0,3

Links

Winston de Greef, Table of n, a(n) for n = 0..385

Formula

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

a(n) ~ exp(exp(-1)) * n^n. - Vaclav Kotesovec, Jul 05 2022

Mathematica

Join[{1}, Table[Sum[k^k * Binomial[n-1, k-1], {k, 1, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Jul 05 2022 *)

Prog

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

Crossrefs

Cf. A355495, A355496.

Cf. A086331.

Sequence in context: A099391 A008785 A375616 * A081918 A062024 A031971

Adjacent sequences: A355491 A355492 A355493 * A355495 A355496 A355497

Keyword

nonn

Author

Seiichi Manyama, Jul 04 2022

Status

approved