OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
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
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}]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 16 2016
STATUS
approved