a(1) = a(2) = a(3) = 1 and a(n) = 24*binomial(n+1, 5) + n*(n^2 - n + 6) for n > 3.

Terms

a(0) =1a(1) =1a(2) =1a(3) =96a(4) =274a(5) =720a(6) =1680a(7) =3520a(8) =6750a(9) =12048a(10) =20284a(11) =32544a(12) =50154a(13) =74704a(14) =108072a(15) =152448a(16) =210358a(17) =284688a(18) =378708a(19) =496096a(20) =640962a(21) =817872a(22) =1031872a(23) =1288512a(24) =1593870a(25) =1954576a(26) =2377836a(27) =2871456a(28) =3443866a(29) =4104144