a(n) = n*(n+1)*(n+2)^2/6.

Terms

a(0) =0a(1) =3a(2) =16a(3) =50a(4) =120a(5) =245a(6) =448a(7) =756a(8) =1200a(9) =1815a(10) =2640a(11) =3718a(12) =5096a(13) =6825a(14) =8960a(15) =11560a(16) =14688a(17) =18411a(18) =22800a(19) =27930a(20) =33880a(21) =40733a(22) =48576a(23) =57500a(24) =67600a(25) =78975a(26) =91728a(27) =105966a(28) =121800a(29) =139345