OFFSET
0,7
FORMULA
a(n) = n! * Sum_{k=0..floor(n/5)} (-1/5!)^k * binomial(n-4*k,k)/(n-4*k)!.
a(n) = a(n-1) - binomial(n-1,4) * a(n-5) for n > 4.
MATHEMATICA
m = 28; Range[0, m]! * CoefficientList[Series[Exp[x - x^5/5!], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^5/5!)))
(PARI) a(n) = n!*sum(k=0, n\5, (-1/5!)^k*binomial(n-4*k, k)/(n-4*k)!);
(PARI) a(n) = if(n<5, 1, a(n-1)-binomial(n-1, 4)*a(n-5));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 26 2022
STATUS
approved