A308538 a(n) = exp(1) * Sum_{k>=0} (-1)^k*(k*(k + 1))^n/k!.

1, -1, 3, -11, -47, 2111, -18589, -671803, 24578625, 328227551, -44122149981, -17436709707, 129678315723089, -1671362093527073, -621466693739336509, 16245508786340273349, 4705502566521408713473, -172007688705762528111809, -54084940569279187064459581

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*A000587(2*n-k).

Mathematica

Table[Exp[1] Sum[(-1)^k (k (k + 1))^n/k!, {k, 0, Infinity}], {n, 0, 18}]
Table[Sum[Binomial[n, k] BellB[2 n - k, -1], {k, 0, n}], {n, 0, 18}]

Crossrefs

Cf. A000587, A020556, A090211, A094577.

Sequence in context: A167564 A295833 A191344 * A181278 A126180 A121139

Adjacent sequences: A308535 A308536 A308537 * A308539 A308540 A308541

Keyword

sign

Author

Ilya Gutkovskiy, Jun 06 2019

Status

approved