OFFSET
0,2
FORMULA
a(n) = n! * Sum_{k=0..n} (-3)^(n-k) * (n-k)^k/k!.
a(0) = 1 and a(n) = -3 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.
MATHEMATICA
With[{nn=30}, CoefficientList[Series[1/(1+3x Exp[x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 21 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*exp(x))))
(PARI) a(n) = n!*sum(k=0, n, (-3)^(n-k)*(n-k)^k/k!);
(PARI) a(n) = if(n==0, 1, -3*n*sum(k=0, n-1, binomial(n-1, k)*a(k)));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 19 2022
STATUS
approved