a(n) = (n+1)*(n+2)^2*(n+3)*(7n^2 + 28n + 30)/360.

Terms

a(0) =1a(1) =13a(2) =76a(3) =295a(4) =889a(5) =2254a(6) =5040a(7) =10242a(8) =19305a(9) =34243a(10) =57772a(11) =93457a(12) =145873a(13) =220780a(14) =325312a(15) =468180a(16) =659889a(17) =912969a(18) =1242220a(19) =1664971a(20) =2201353a(21) =2874586a(22) =3711280a(23) =4741750a(24) =6000345a(25) =7525791a(26) =9361548a(27) =11556181a(28) =14163745a(29) =17244184