OFFSET
0,5
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} (-1/6)^k * binomial(n-2*k,k)/(n-2*k)!.
a(n) = a(n-1) - binomial(n-1,2) * a(n-3) for n > 2.
MATHEMATICA
m = 27; Range[0, m]! * CoefficientList[Series[Exp[x - x^3/6], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^3/6)))
(PARI) a(n) = n!*sum(k=0, n\3, (-1/3!)^k*binomial(n-2*k, k)/(n-2*k)!);
(PARI) a(n) = if(n<3, 1, a(n-1)-binomial(n-1, 2)*a(n-3));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 26 2022
STATUS
approved