A368555 a(n) = Sum_{k=0..n} k! * 3^(n-k).
1, 4, 14, 48, 168, 624, 2592, 12816, 78768, 599184, 5426352, 56195856, 647589168, 8169788304, 111687656112, 1642737336336, 25851001897008, 433240433787024, 7702095007089072, 144751385430099216, 2867156164466937648, 59692410665110252944
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, k!*3^(n-k));
Formula
a(0) = 1; a(n) = 3*a(n-1) + n!.
a(n) = (n+3)*a(n-1) - 3*n*a(n-2).
a(n) ~ n!. - Vaclav Kotesovec, Jan 13 2024