OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
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).
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}]
PROG
(PARI) x='x+O('x^50); concat([0, 0], Vec(serlaplace(-sinh(x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 17 2016
STATUS
approved