a(n) = (n+1)^2*(n+2)*(n+3)*(3*n+4)/24.

Terms

a(0) =1a(1) =14a(2) =75a(3) =260a(4) =700a(5) =1596a(6) =3234a(7) =6000a(8) =10395a(9) =17050a(10) =26741a(11) =40404a(12) =59150a(13) =84280a(14) =117300a(15) =159936a(16) =214149a(17) =282150a(18) =366415a(19) =469700a(20) =595056a(21) =745844a(22) =925750a(23) =1138800a(24) =1389375a(25) =1682226a(26) =2022489a(27) =2415700a(28) =2867810a(29) =3385200