a(n) = (n+1)(n+2)^3*(n+3)(n+4)(5n^2 + 16n + 15)/1440.

Terms

a(0) =1a(1) =27a(2) =268a(3) =1575a(4) =6678a(5) =22638a(6) =65184a(7) =165726a(8) =381975a(9) =813241a(10) =1621620a(11) =3060421a(12) =5511324a(13) =9531900a(14) =15915264a(15) =25763772a(16) =40578813a(17) =62368887a(18) =93778300a(19) =138238947a(20) =200147794a(21) =285072810a(22) =399990240a(23) =553556250a(24) =756416115a(25) =1021554261