A triangle of polynomial coefficients:p(x,n)=Sum[(2*k + 1)^n*k!*Binomial[x, k], {k, 0, n}].

Terms

a(0) =1a(1) =1a(2) =3a(3) =1a(4) =-16a(5) =25a(6) =1a(7) =588a(8) =-904a(9) =343a(10) =1a(11) =-35108a(12) =65593a(13) =-36965a(14) =6561a(15) =1a(16) =3541662a(17) =-7450307a(18) =5299298a(19) =-1551461a(20) =161051a(21) =1a(22) =-539667860a(23) =1239476145a(24) =-1027098387a(25) =393094596a(26) =-70630574a(27) =4826809a(28) =1a(29) =115929493398