A351769 a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling1(n, k) * k^(k+n).

1, 1, 17, 827, 79368, 12623124, 3002832110, 998401869464, 442148442609152, 251578963946182968, 178846127724854653704, 155339277405600252114072, 161863497852092601156187152, 199286757107586767535516731832, 286210094619439661737214469710088

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

Cf. A351180, A351181.

Sequence in context: A191963 A328138 A351181 * A139091 A262634 A173983

Adjacent sequences: A351766 A351767 A351768 * A351770 A351771 A351772

Keyword

nonn

Author

Vaclav Kotesovec, Feb 18 2022

Status

approved