OFFSET
0,2
FORMULA
G.f. A(x) satisfies: A(x) = 1 - x * ( A(x) - 4 * A(x/(1 - x)) / (1 - x) ).
a(n) = exp(-4) * Sum_{k>=0} 4^k * (k-1)^n / k!.
a(0) = 1; a(n) = -a(n-1) + 4 * Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).
MATHEMATICA
nmax = 21; CoefficientList[Series[Exp[4 (Exp[x] - 1) - x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -a[n - 1] + 4 Sum[Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 04 2023
STATUS
approved