a(n) = n*(n+1)*(n+2)*(n+3)*(2*n^2+6*n+7)/360.

Terms

a(0) =0a(1) =1a(2) =9a(3) =43a(4) =147a(5) =406a(6) =966a(7) =2058a(8) =4026a(9) =7359a(10) =12727a(11) =21021a(12) =33397a(13) =51324a(14) =76636a(15) =111588a(16) =158916a(17) =221901a(18) =304437a(19) =411103a(20) =547239a(21) =719026a(22) =933570a(23) =1198990a(24) =1524510a(25) =1920555a(26) =2398851a(27) =2972529a(28) =3656233a(29) =4466232