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A295623
a(n) = n! * [x^n] exp(n*x*exp(x)).
2
1, 1, 8, 90, 1424, 28900, 716292, 20972098, 708317248, 27108056808, 1159375192100, 54799938951934, 2836735081572240, 159606310760007436, 9698172715195196260, 632924646574215596850, 44153807025286701187328, 3278903858941755472870864, 258247909552273997037934788
OFFSET
0,3
LINKS
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