OFFSET
0,3
FORMULA
a(n) = (n-1) * a(n-1) + (n-2) * a(n-2) + (n-3) * a(n-3) + (n-6) * a(n-4) - 3 * a(n-5) - 3 * a(n-6) - 3 * a(n-7) + 4 for n > 6.
a(n) ~ n! * (1 + 1/n^3 + 3/n^4 + 7/n^5 + 31/(2*n^6) + 77/(2*n^7) + 133/n^8 + 3913/(6*n^9) + 7473/(2*n^10) + ...). - Vaclav Kotesovec, Nov 25 2022
G.f.: Sum_{k>=0} k! * x^k/(1-x^4)^(k+1). - Seiichi Manyama, Feb 26 2024
MATHEMATICA
Table[Sum[(n-3k)!/k!, {k, 0, Floor[n/4]}], {n, 0, 30}] (* Harvey P. Dale, Apr 23 2023 *)
PROG
(PARI) a(n) = sum(k=0, n\4, (n-3*k)!/k!);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 19 2022
STATUS
approved