Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

Terms

a(0) =1a(1) =1a(2) =4a(3) =1a(4) =8a(5) =8a(6) =1a(7) =12a(8) =32a(9) =16a(10) =1a(11) =16a(12) =72a(13) =96a(14) =32a(15) =1a(16) =20a(17) =128a(18) =304a(19) =256a(20) =64a(21) =1a(22) =24a(23) =200a(24) =704a(25) =1056a(26) =640a(27) =128a(28) =1a(29) =28