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

Terms

a(0) =1a(1) =-1a(2) =1a(3) =1a(4) =-1a(5) =1a(6) =-1a(7) =0a(8) =0a(9) =1a(10) =1a(11) =0a(12) =-3a(13) =2a(14) =1a(15) =-1a(16) =5a(17) =-5a(18) =-5a(19) =5a(20) =1a(21) =1a(22) =-5a(23) =30a(24) =-35a(25) =0a(26) =9a(27) =1a(28) =-1a(29) =-56