A277473 E.g.f.: -exp(x)*LambertW(-x).

0, 1, 4, 18, 116, 1060, 12702, 187810, 3296120, 66897288, 1540762010, 39693752494, 1130866726596, 35300006582620, 1198036854980630, 43921652697277170, 1729775120233353968, 72831210167041246480, 3264674481128340280242, 155220967397580333229270

Offset: 0

Author

Vaclav Kotesovec, Oct 17 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A000169, A069856, A086331, A277474.

Partial sums of A038051.

Programs

Mathematica

CoefficientList[Series[-Exp[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[Binomial[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]

PARI

x='x+O('x^50); concat([0], Vec(serlaplace(-exp(x)*lambertw(-x)))) \\ G. C. Greubel, Jun 11 2017

Formula

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

a(n) ~ exp(exp(-1)) * n^(n-1).