a(n) = (n+1)(n+2)^3*(n+3)(13n^2 + 37n + 30)/720.

Terms

a(0) =1a(1) =24a(2) =208a(3) =1075a(4) =4053a(5) =12348a(6) =32256a(7) =75006a(8) =159225a(9) =314116a(10) =583440a(11) =1030393a(12) =1743469a(13) =2843400a(14) =4491264a(15) =6897852a(16) =10334385a(17) =15144672a(18) =21758800a(19) =30708447a(20) =42643909a(21) =58352932a(22) =78781440a(23) =105056250a(24) =138509865a(25) =180707436a(26) =233475984