OFFSET
0,3
FORMULA
a(n) = exp(1) * Sum_{k>=0} (-1)^k*(2*k + 1)^n/k!.
a(n) = Sum_{k=0..n} binomial(n,k)*2^k*A000587(k).
MATHEMATICA
nmax = 23; CoefficientList[Series[Exp[1 + x - Exp[2 x]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Exp[1] Sum[(-1)^k (2 k + 1)^n/k!, {k, 0, Infinity}], {n, 0, 23}]
Table[Sum[Binomial[n, k] 2^k BellB[k, -1], {k, 0, n}], {n, 0, 23}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 13 2019
STATUS
approved