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A292914 a(n) = n! * [x^n] exp(exp(n*x)-1). 8
1, 1, 8, 135, 3840, 162500, 9471168, 722247211, 69457674240, 8192781080883, 1159750000000000, 193603940326506270, 37568854100470136832, 8372811803057822746561, 2121274569058397526065152, 605589097505502777099609375, 193324500041805946527313559552, 68549156597838159410025756211308 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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

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}]]

CROSSREFS

Main diagonal of A292913.

Cf. A000110.

Sequence in context: A069988 A229237 A291699 * A072072 A195614 A131927

Adjacent sequences:  A292911 A292912 A292913 * A292915 A292916 A292917

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 26 2017

STATUS

approved

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Last modified June 14 04:54 EDT 2021. Contains 345018 sequences. (Running on oeis4.)