OFFSET
0,2
FORMULA
a(n) = exp(2) * (-1)^n * Sum_{k>=0} (-2)^k * (k - 1)^n / k!.
a(0) = 1; a(n) = a(n-1) + 2 * Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n-1,k) * a(k).
MATHEMATICA
nmax = 25; CoefficientList[Series[Exp[2 (1 - Exp[-x]) + x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = a[n - 1] + 2 Sum[(-1)^(n - k - 1) Binomial[n - 1, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 25}]
PROG
(PARI) my(N=33, x='x+O('x^N)); Vec(serlaplace(exp(2 * (1 - exp(-x)) + x))) \\ Joerg Arndt, Jul 04 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jul 03 2020
STATUS
approved