A358494 a(n) = Sum_{k=0..floor(n/5)} (n-4*k)!/k!.
1, 1, 2, 6, 24, 121, 722, 5046, 40344, 363000, 3629521, 39921843, 479041932, 6227383740, 87181920360, 1307714287321, 20923268909764, 355693655298260, 6402460885833720, 121646408103159240, 2432922931206035521, 51091297862251106885, 1124007130194903158430
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n\5, (n-4*k)!/k!);
Formula
a(n) = (n-1) * a(n-1) + (n-2) * a(n-2) + (n-3) * a(n-3) + (n-4) * a(n-4) + (n-8) * a(n-5) - 4 * a(n-6) - 4 * a(n-7) - 4 * a(n-8) - 4 * a(n-9) + 5 for n > 8.
G.f.: Sum_{k>=0} k! * x^k/(1-x^5)^(k+1). - Seiichi Manyama, Feb 26 2024