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

0,3

Links

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

Formula

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

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

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}]

Prog

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

Crossrefs

Cf. A000169, A069856, A086331, A277474.

Partial sums of A038051.

Sequence in context: A220223 A137567 A326261 * A278994 A223008 A162224

Adjacent sequences: A277470 A277471 A277472 * A277474 A277475 A277476

Keyword

nonn

Author

Vaclav Kotesovec, Oct 17 2016

Status

approved