OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..n} (-4 * (n-k))^k/k!.
a(0) = 1 and a(n) = n * Sum_{k=0..n-1} (-4)^(n-1-k) * binomial(n-1,k) * a(k) for n > 0.
MATHEMATICA
a[0] = 1; a[n_] := n!*Sum[(-4*(n - k))^k/k!, {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Feb 19 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(-4*x))))
(PARI) a(n) = n!*sum(k=0, n, (-4*(n-k))^k/k!);
(PARI) a(n) = if(n==0, 1, n*sum(k=0, n-1, (-4)^(n-1-k)*binomial(n-1, k)*a(k)));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 19 2022
STATUS
approved