OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..n} (-2 * (n-k))^k / k!.
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k * (-2)^(k-1) * a(n-k).
MATHEMATICA
nmax = 21; CoefficientList[Series[1/(1 - x Exp[-2 x]), {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[n! Sum[(-2 (n - k))^k/k!, {k, 0, n}], {n, 1, 21}]]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k (-2)^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Aug 09 2020
STATUS
approved