a(n) = 13 + Sum_{j=4..n+3} j!.

Terms

a(0) =13a(1) =37a(2) =157a(3) =877a(4) =5917a(5) =46237a(6) =409117a(7) =4037917a(8) =43954717a(9) =522956317a(10) =6749977117a(11) =93928268317