A295623 a(n) = n! * [x^n] exp(n*x*exp(x)).

1, 1, 8, 90, 1424, 28900, 716292, 20972098, 708317248, 27108056808, 1159375192100, 54799938951934, 2836735081572240, 159606310760007436, 9698172715195196260, 632924646574215596850, 44153807025286701187328, 3278903858941755472870864, 258247909552273997037934788

Offset: 0

Author

Ilya Gutkovskiy, Nov 24 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..360
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000248, A242817, A275707, A351765.

Programs

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}]

PARI

a(n) = sum(k=0, n, n^k*k^(n-k)*binomial(n, k)); \\ Seiichi Manyama, Jul 04 2022

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)