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

Offset: 0

Author

Ilya Gutkovskiy, Jan 22 2021

Keywords

• nonn

Crossrefs

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

Programs

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}]]

Formula

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