a(n) = (n^2 - 3*n + 6)*binomial(n+2,3)/4.

Terms

a(0) =0a(1) =1a(2) =4a(3) =15a(4) =50a(5) =140a(6) =336a(7) =714a(8) =1380a(9) =2475a(10) =4180a(11) =6721a(12) =10374a(13) =15470a(14) =22400a(15) =31620a(16) =43656a(17) =59109a(18) =78660a(19) =103075a(20) =133210a(21) =170016a(22) =214544a(23) =267950a(24) =331500a(25) =406575a(26) =494676a(27) =597429a(28) =716590a(29) =854050