OFFSET
0,3
FORMULA
a(n) = n! * [x^n] exp(exp(n*x) - x - 1).
a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * n^k * Bell(k).
MATHEMATICA
Table[Exp[-1] Sum[(n k - 1)^n/k!, {k, 0, Infinity}], {n, 0, 16}]
Join[{1}, Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k], {k, 0, n}], {n, 1, 16}]]
Table[n! SeriesCoefficient[Exp[Exp[n x] - x - 1], {x, 0, n}], {n, 0, 16}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 19 2019
STATUS
approved