a(n) = 1 + (144 + (50 + (35 + (10 + n)*n)*n)*n)*n/120.

Terms

a(0) =1a(1) =3a(2) =9a(3) =25a(4) =61a(5) =132a(6) =259a(7) =470a(8) =801a(9) =1297a(10) =2013a(11) =3015a(12) =4381a(13) =6202a(14) =8583a(15) =11644a(16) =15521a(17) =20367a(18) =26353a(19) =33669a(20) =42525a(21) =53152a(22) =65803a(23) =80754a(24) =98305a(25) =118781a(26) =142533a(27) =169939a(28) =201405a(29) =237366