OFFSET
0,5
FORMULA
a(n) = binomial(n,3) * a(n-3) - Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 2.
a(n) = n! * Sum_{k=0..floor(n/3)} (-k-1)^(n-3*k)/(6^k*(n-3*k)!). - Seiichi Manyama, Aug 21 2024
MATHEMATICA
m = 23; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^3/6), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-x^3/6)))
(PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m))*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 3);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 11 2022
STATUS
approved