a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(5*n^2 + 19*n + 15)/360.

Terms

a(0) =1a(1) =13a(2) =73a(3) =273a(4) =798a(5) =1974a(6) =4326a(7) =8646a(8) =16071a(9) =28171a(10) =47047a(11) =75439a(12) =116844a(13) =175644a(14) =257244a(15) =368220a(16) =516477a(17) =711417a(18) =964117a(19) =1287517a(20) =1696618a(21) =2208690a(22) =2843490a(23) =3623490a(24) =4574115a(25) =5723991a(26) =7105203a(27) =8753563a(28) =10708888a(29) =13015288