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

Terms

a(0) =1a(1) =4a(2) =15a(3) =58a(4) =241a(5) =1056a(6) =4879a(7) =23710a(8) =120033a(9) =635356a(10) =3478351a(11) =19796514a(12) =115988305a(13) =703052728a(14) =4372581711a(15) =28022140486a(16) =183804777409