a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)^2*(n+5)(3n^2 + 13n + 15)/43200.

Terms

a(0) =1a(1) =31a(2) =371a(3) =2646a(4) =13524a(5) =54684a(6) =185724a(7) =551034a(8) =1467609a(9) =3578575a(10) =8107099a(11) =17257604a(12) =34826064a(13) =67098864a(14) =124140528a(15) =221594796a(16) =383151321a(17) =643861911a(18) =1054526011a(19) =1687405258a(20) =2643571700a(21) =4062243900a(22) =6132519900a(23) =9107976150a(24) =13324667265a(25) =19223133111a(26) =27375097491