a(n) = n! * Sum_{k=0..n} binomial(k+3,4) / k!.

Terms

a(0) =0a(1) =1a(2) =7a(3) =36a(4) =179a(5) =965a(6) =5916a(7) =41622a(8) =333306a(9) =3000249a(10) =30003205a(11) =330036256a(12) =3960436437a(13) =51485675501a(14) =720799459394