a(n) = (n+2)*(n+1)*(n^6-12*n^5+70*n^4-210*n^3+409*n^2-378*n+360)/720.

Terms

a(0) =1a(1) =2a(2) =6a(3) =20a(4) =70a(5) =252a(6) =896a(7) =2976a(8) =8955a(9) =24310a(10) =60038a(11) =136500a(12) =289016a(13) =575680a(14) =1087920a(15) =1964384a(16) =3408789a(17) =5712426a(18) =9282070a(19) =14674100a(20) =22635690a(21) =34153988a(22) =50514256a(23) =73368000a(24) =104812175a(25) =147480606a(26) =204648822a(27) =280353556a(28) =379528220a(29) =508155720