a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(2n+5)/720.

Terms

a(0) =1a(1) =14a(2) =90a(3) =385a(4) =1274a(5) =3528a(6) =8568a(7) =18810a(8) =38115a(9) =72358a(10) =130130a(11) =223587a(12) =369460a(13) =590240a(14) =915552a(15) =1383732a(16) =2043621a(17) =2956590a(18) =4198810a(19) =5863781a(20) =8065134a(21) =10939720a(22) =14651000a(23) =19392750a(24) =25393095a(25) =32918886a(26) =42280434a(27) =53836615a(28) =68000360