A292914 a(n) = n! * [x^n] exp(exp(n*x)-1).

1, 1, 8, 135, 3840, 162500, 9471168, 722247211, 69457674240, 8192781080883, 1159750000000000, 193603940326506270, 37568854100470136832, 8372811803057822746561, 2121274569058397526065152, 605589097505502777099609375, 193324500041805946527313559552, 68549156597838159410025756211308

Offset: 0

Author

Ilya Gutkovskiy, Sep 26 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..258

Crossrefs

Main diagonal of A292913.

Cf. A000110.

Programs

Maple

a:= n-> n^n * combinat[bell](n):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 26 2017

Mathematica

Table[n! SeriesCoefficient[Exp[Exp[n x] - 1], {x, 0, n}], {n, 0, 17}]
Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-((-1)^(k + 1) (k - 1) + k + 3) n x/4, 1, {k, 0, n}]), {x, 0, n}], {n, 0, 17}]
Join[{1}, Table[n^n BellB[n], {n, 1, 17}]]

Formula

a(n) = [x^n] 1/(1 - n*x/(1 - n*x/(1 - n*x/(1 - 2*n*x/(1 - n*x/(1 - 3*n*x/(1 - n*x/(1 - 4*n*x/(1 - ...))))))))), a continued fraction.

a(n) = exp(-1)*n^n*Sum_{k>=0} k^n/k!.

a(n) = A292913(n,n).

a(n) = n^n * Bell(n). - Alois P. Heinz, Sep 26 2017