a(n) = (n+1)(n+2)^3*(n+3)(n^2 + 4n + 5)/120.

Terms

a(0) =1a(1) =18a(2) =136a(3) =650a(4) =2331a(5) =6860a(6) =17472a(7) =39852a(8) =83325a(9) =162382a(10) =298584a(11) =522886a(12) =878423a(13) =1423800a(14) =2236928a(15) =3419448a(16) =5101785a(17) =7448874a(18) =10666600a(19) =15008994a(20) =20786227a(21) =28373444a(22) =38220480a(23) =50862500a(24) =66931605a(25) =87169446a(26) =112440888a(27) =143748766