OFFSET
0,3
FORMULA
a(n) = n! * [x^n] exp(n*(exp(x) - 1 - x)).
a(n) = Sum_{k=0..n} binomial(n,k) * (-n)^(n-k) * BellPolynomial_k(n).
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n (Exp[x] - 1 - x)], {x, 0, n}], {n, 0, 19}]
Unprotect[Power]; 0^0 = 1; Table[Sum[Binomial[n, k] (-n)^(n - k) BellB[k, n], {k, 0, n}], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 13 2020
STATUS
approved