A358498 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)!.
1, 1, 2, 7, 25, 122, 727, 5065, 40442, 363607, 3633865, 39957242, 479365207, 6230654665, 87218248442, 1308153733207, 20929020542665, 355774646344442, 6403681859461207, 121666029429374665, 2433257782822984442, 51097345853568901207, 1124122393807037054665
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..449
Programs
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PARI
a(n) = sum(k=0, n\3, (n-3*k)!);
Formula
a(n) = n * a(n-1) + a(n-3) - n * a(n-4) for n > 3.
a(n) ~ n! * (1 + 1/n^3 + 3/n^4 + 7/n^5 + 16/n^6 + 46/n^7 + 203/n^8 + 1178/n^9 + 7242/n^10 + ...), for coefficients see A143817. - Vaclav Kotesovec, Nov 24 2022