A360193 a(n) = Sum_{k=0..n} (k-1)^(k-1) * binomial(n,k).

-1, 0, 2, 9, 52, 445, 5166, 75019, 1300776, 26167257, 598577770, 15337224991, 435020120316, 13529095809541, 457727913937854, 16736043791509995, 657590281425958096, 27631245762003186865, 1236355641557737359570, 58689534518861119967287

Offset

0,3

Links

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

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: -exp(x + LambertW(-x)).

E.g.f.: x * exp(x) / LambertW(-x).

a(n) ~ exp(exp(-1)-1) * n^(n-1). - Vaclav Kotesovec, Mar 06 2023

Prog

(PARI) a(n) = sum(k=0, n, (k-1)^(k-1)*binomial(n, k));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x+lambertw(-x))))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(x*exp(x)/lambertw(-x)))

Crossrefs

Cf. A088957, A105785, A177885, A277473.

Sequence in context: A121678 A124347 A360743 * A347774 A360718 A266469

Adjacent sequences: A360190 A360191 A360192 * A360194 A360195 A360196

Keyword

sign,easy

Author

Seiichi Manyama, Mar 05 2023

Status

approved