A360611 Expansion of Sum_{k>=0} (k * x * (1 + x))^k.

1, 1, 5, 35, 341, 4230, 63844, 1135753, 23273363, 539881365, 13986073419, 400227436252, 12538263892232, 426810214125441, 15687071552060221, 619144491880324087, 26117514728711229877, 1172635546310430028562, 55833864788507320490268

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} (n-k)^(n-k) * binomial(n-k,k).

a(n) ~ exp(exp(-1)) * n^n. - Vaclav Kotesovec, Feb 14 2023

Mathematica

Flatten[{1, Table[Sum[Binomial[n-k, k] * (n-k)^(n-k), {k, 0, n/2}], {n, 1, 20}]}] (* Vaclav Kotesovec, Feb 14 2023 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+x))^k))
(PARI) a(n) = sum(k=0, n\2, (n-k)^(n-k)*binomial(n-k, k));

Crossrefs

Cf. A355494, A360592.

Sequence in context: A262248 A346666 A369724 * A201367 A233860 A258902

Adjacent sequences: A360608 A360609 A360610 * A360612 A360613 A360614

Keyword

nonn

Author

Seiichi Manyama, Feb 14 2023

Status

approved