A277464 Expansion of e.g.f. cosh(x)/(1 + LambertW(-x)).

1, 1, 5, 30, 281, 3400, 50557, 890120, 18101617, 417464064, 10764826421, 306893014912, 9584448407305, 325407839778944, 11933432488693549, 470087171351873280, 19796492491889197025, 887518214183286390784, 42202928616264032249701, 2121583256369642798845952

Offset: 0

Author

Vaclav Kotesovec, Oct 16 2016

Keywords

• nonn

Links

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

Crossrefs

Cf. A000312, A069856, A086331, A277462, A277463.

Programs

Mathematica

CoefficientList[Series[Cosh[x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
Table[(1+(-1)^n + Sum[(1+(-1)^(n-k)) * Binomial[n,k] * k^k, {k, 1, n}])/2, {n, 0, 25}]

PARI

x='x+O('x^50); Vec(serlaplace(cosh(x)/(1 + lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017

PARI

a(n) = sum(k=0, n\2, (n-2*k)^(n-2*k)*binomial(n, 2*k)); \\ Seiichi Manyama, Feb 15 2023

Formula

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

a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-2*k) * binomial(n,2*k). - Seiichi Manyama, Feb 15 2023