a(n) = (n+1)*(n+2)^3*(n+3)*(2n+3)*(2n+5)/360.

Terms

a(0) =1a(1) =21a(2) =168a(3) =825a(4) =3003a(5) =8918a(6) =22848a(7) =52326a(8) =109725a(9) =214291a(10) =394680a(11) =692055a(12) =1163799a(13) =1887900a(14) =2968064a(15) =4539612a(16) =6776217a(17) =9897537a(18) =14177800a(19) =19955397a(20) =27643539a(21) =37742034a(22) =50850240a(23) =67681250a(24) =89077365a(25) =116026911a(26) =149682456a(27) =191380483