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A308647
a(n) = exp(1) * Sum_{k>=0} (-1)^k*k^(2*n+1)/k!.
1
-1, 1, -2, -9, 267, -2180, -50533, 1966797, 8638718, -2540956509, 27172288399, 5592543175252, -168392610536153, -20819319685262839, 1122009166836993406, 127595724180314195839, -9985347479130060737373, -1244077225312583088164916, 120225865637787689310572899, 18462990063073814590636032245
OFFSET
0,3
LINKS
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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 13 2019
STATUS
approved