OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..213
FORMULA
a(n) ~ c * r^n * (1 + r*exp(1 + 1/r))^n * n^(2*n) / exp(2*n), where r = 0.937997555632908331545534056235449048849427140626270261830822459734975609... is the root of the equation r + exp(-1 - 1/r) = -LambertW(-1, -r*exp(-r)) and c = 0.9367460233410089838603007174937882495902299959682250862650092226619624... - Vaclav Kotesovec, Feb 18 2022
E.g.f.: Sum_{k>=0} (-k * log(1 - k*x))^k / k!. - Seiichi Manyama, Jun 02 2022
MATHEMATICA
Table[Sum[k^(k+n) * StirlingS1[n, k] * (-1)^(n-k), {k, 0, n}], {n, 0, 20}]
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*stirling(n, k, 1)*k^(k+n)); \\ Michel Marcus, Feb 19 2022
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k*log(1-k*x))^k/k!))) \\ Seiichi Manyama, Jun 02 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 18 2022
STATUS
approved