A308647 a(n) = exp(1) * Sum_{k>=0} (-1)^k*k^(2*n+1)/k!.

-1, 1, -2, -9, 267, -2180, -50533, 1966797, 8638718, -2540956509, 27172288399, 5592543175252, -168392610536153, -20819319685262839, 1122009166836993406, 127595724180314195839, -9985347479130060737373, -1244077225312583088164916, 120225865637787689310572899, 18462990063073814590636032245

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Complementary Bell Number

Formula

a(n) = Sum_{k=0..2*n+1} (-1)^k*Stirling2(2*n+1,k).

a(n) = A000587(2*n+1).

Mathematica

Table[Exp[1] Sum[(-1)^k k^(2 n + 1)/k!, {k, 0, Infinity}], {n, 0, 19}]
Table[BellB[2 n + 1, -1], {n, 0, 19}]

Crossrefs

Cf. A000587, A099977, A308646.

Sequence in context: A011823 A122894 A042675 * A015177 A005271 A258668

Adjacent sequences: A308644 A308645 A308646 * A308648 A308649 A308650

Keyword

sign

Author

Ilya Gutkovskiy, Jun 13 2019

Status

approved