OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..360
N. J. A. Sloane, Transforms
FORMULA
a(n) = n! * [x^n] exp(n*Sum_{k>=1} x^k/(k - 1)!).
From Seiichi Manyama, Jul 05 2022: (Start)
a(n) = [x^n] Sum_{k>=0} (n * x)^k/(1 - k*x)^(k+1).
a(n) = Sum_{k=0..n} n^k * k^(n-k) * binomial(n,k). (End)
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n x Exp[x]], {x, 0, n}], {n, 0, 18}]
Table[Sum[BellY[n, k, n Range[n]], {k, 0, n}], {n, 0, 18}]
PROG
(PARI) a(n) = sum(k=0, n, n^k*k^(n-k)*binomial(n, k)); \\ Seiichi Manyama, Jul 04 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 24 2017
STATUS
approved