a(n) = (n+2)*(n+1)*(n^2 + 7*n - 12)/24.

Terms

a(0) =-1a(1) =3a(2) =15a(3) =40a(4) =84a(5) =154a(6) =258a(7) =405a(8) =605a(9) =869a(10) =1209a(11) =1638a(12) =2170a(13) =2820a(14) =3604a(15) =4539a(16) =5643a(17) =6935a(18) =8435a(19) =10164a(20) =12144a(21) =14398a(22) =16950a(23) =19825a(24) =23049a(25) =26649a(26) =30653a(27) =35090a(28) =39990a(29) =45384