A277476 E.g.f.: -sinh(x)*LambertW(-x).

0, 0, 2, 6, 40, 340, 3936, 56714, 976704, 19535688, 444743680, 11349643822, 320813048832, 9947821243100, 335700998830848, 12246806941654770, 480247532548624384, 20144008859005187344, 899923326921333301248, 42658767419625168409814, 2138475182252830504796160

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, A277463, A277473, A277475, A277478.

Programs

Mathematica

CoefficientList[Series[-Sinh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[(1 - (-1)^(n-k)) * Binomial[n, k] * k^(k-1)/2, {k, 1, n}], {n, 0, 20}]

PARI

x='x+O('x^50); concat([0,0], Vec(serlaplace(-sinh(x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 07 2017

Formula

a(n) = Sum_{k=1..n} (1 - (-1)^(n-k)) * binomial(n,k) * k^(k-1)/2.

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