A330605 - OEIS

A330605

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

1, 0, 5, 89, 2737, 121399, 7316101, 572218716, 56142822849, 6731180810945, 965898950508901, 163116461798211503, 31969444766902475185, 7187057932197297484108, 1834860441330563739401765, 527403671798720265634312349, 169396494914472404237224898305

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

FORMULA

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

a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * n^k * Bell(k).

MATHEMATICA

Table[Exp[-1] Sum[(n k - 1)^n/k!, {k, 0, Infinity}], {n, 0, 16}]

Join[{1}, Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k], {k, 0, n}], {n, 1, 16}]]

Table[n! SeriesCoefficient[Exp[Exp[n x] - x - 1], {x, 0, n}], {n, 0, 16}]

CROSSREFS

Cf. A000110, A000296, A124311, A292914, A307066, A330604.

Sequence in context: A134497 A358388 A339001 * A028353 A191512 A015085

Adjacent sequences: A330602 A330603 A330604 * A330606 A330607 A330608

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 19 2019

STATUS

approved