a(n) = n*(n+1)*(n+2)*(n^2+7*n+32)/120.

Terms

a(0) =2a(1) =10a(2) =31a(3) =76a(4) =161a(5) =308a(6) =546a(7) =912a(8) =1452a(9) =2222a(10) =3289a(11) =4732a(12) =6643a(13) =9128a(14) =12308a(15) =16320a(16) =21318a(17) =27474a(18) =34979a(19) =44044a(20) =54901a(21) =67804a(22) =83030a(23) =100880a(24) =121680a(25) =145782a(26) =173565a(27) =205436a(28) =241831a(29) =283216