OFFSET
0,3
FORMULA
a(n) = n * (n-1) * (n-2) * a(n-3) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 2.
MATHEMATICA
m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^3), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^3)))
(PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 3);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 11 2022
STATUS
approved