%I #2 Oct 12 2012 14:54:51
%S 4,4,6,0,-2,12,0,-8,30,0,-30,0,4,90,0,-120,0,34,315,0,-525,0,231,0,
%T -17,1260,0,-2520,0,1512,0,-248,5670,0,-13230,0,10080,0,-2640,0,124,
%U 28350,0,-75600,0,69930,0,-25440,0,2764
%N A triangular sequence of coefficients of a PolyLog functional polynomials: p(x.n)=16*x^(n + 1)*PolyLog[ -n, (1 - x)/(1 + x)]/((1 + x)*(1 - x)).
%C Row sums are all 4.
%F p(x.n)=16*x^(n + 1)*PolyLog[ -n, (1 - x)/(1 + x)]/((1 + x)*(1 - x)); t(n,m)=coefficients(p(x,n).
%e {4},
%e {4},
%e {6, 0, -2},
%e {12, 0, -8},
%e {30, 0, -30, 0, 4},
%e {90, 0, -120, 0, 34},
%e {315, 0, -525, 0, 231, 0, -17},
%e {1260, 0, -2520, 0, 1512, 0, -248},
%e {5670, 0, -13230, 0, 10080, 0, -2640, 0, 124},
%e {28350, 0, -75600, 0, 69930, 0, -25440, 0, 2764}
%t Clear[w, p]; p[x_, n_] = 16*x^(n + 1)*PolyLog[ -n, (1 - x)/(1 + x)]/((1 + x)*(1 - x)); Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}]; Flatten[%]
%K sign,uned
%O 1,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 15 2008