A340822 - OEIS

A340822

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

1, 3, 43, 1211, 54812, 3572775, 313493737, 35368945463, 4962511954307, 844198388785291, 170675800745636572, 40352181663578992883, 11008690527354504977193, 3426969405868832970281647, 1205708016597226199323015459, 475502109963529414669658708847

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n) = Sum_{k=0..n} binomial(n,k) * Bell(2*n-k) * n^k.

MATHEMATICA

Table[Exp[-1] Sum[(k (k + n))^n/k!, {k, 0, Infinity}], {n, 0, 15}]

Join[{1}, Table[Sum[Binomial[n, k] BellB[2 n - k] n^k, {k, 0, n}], {n, 1, 15}]]

CROSSREFS

Cf. A000110, A020557, A094577, A134980, A334242, A340823.

Sequence in context: A302664 A201784 A364498 * A355004 A303159 A274387

Adjacent sequences: A340819 A340820 A340821 * A340823 A340824 A340825

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 22 2021

STATUS

approved