a(n) = n! * Sum_{k=0..n} binomial(k+2,3) / k!.

Terms

a(0) =0a(1) =1a(2) =6a(3) =28a(4) =132a(5) =695a(6) =4226a(7) =29666a(8) =237448a(9) =2137197a(10) =21372190a(11) =235094376a(12) =2821132876a(13) =36674727843a(14) =513446190362