A277474 E.g.f.: -exp(-x)*LambertW(-x).

0, 1, 0, 6, 36, 380, 4830, 74382, 1342712, 27825912, 651274650, 16994464850, 489240628932, 15404364096420, 526634857318934, 19428038813967630, 769280055136105200, 32543192449030871792, 1464827827285673677746, 69903432558329996409642, 3525344776953738276010940

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, A277473.

Programs

Mathematica

CoefficientList[Series[-Exp[-x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[(-1)^(n-k)*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, Nov 07 2017

Formula

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

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