a(n) = Sum_{k=3..n} (k-1)!*C(n,k)/2.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =7a(5) =37a(6) =197a(7) =1172a(8) =8018a(9) =62814a(10) =556014a(11) =5488059a(12) =59740609a(13) =710771275a(14) =9174170011a(15) =127661752406