%I #2 Mar 30 2012 17:34:27
%S 1,1,1,1,2,1,1,4,4,1,1,5,9,5,1,1,6,17,17,6,1,1,7,30,56,30,7,1,1,8,52,
%T 191,191,52,8,1,1,9,91,659,1288,659,91,9,1,1,10,163,2241,7953,7953,
%U 2241,163,10,1,1,11,300,7438,44355,78382,44355,7438,300,11,1,1,12,566,24103
%N Shifted Pascal sequence: p(x,n)=(1 + x)^(n + 1) + If[n < 2, 0, x*((1 - x)^(n + 1)*PolyLog[ -n, x]/x + (1 + x)^(n - 1))/2].
%C Row sums are: {1, 2, 4, 10, 21, 48, 132, 504, 2808, 20736, 182592, 1816704}.
%F p(x,n)=(1 + x)^(n + 1) + If[n < 2, 0, x*((1 - x)^(n + 1)*PolyLog[ -n, x]/x + (1 + x)^(n - 1))/2]; t(n,m)=coefficients(p(x,n)).
%e {1}, {1, 1}, {1, 2, 1}, {1, 4, 4, 1}, {1, 5, 9, 5, 1}, {1, 6, 17, 17, 6, 1}, {1, 7, 30, 56, 30, 7, 1}, {1, 8, 52, 191, 191, 52, 8, 1}, {1, 9, 91, 659, 1288, 659, 91, 9, 1}, {1, 10, 163, 2241, 7953, 7953, 2241, 163, 10, 1}, {1, 11, 300, 7438, 44355, 78382, 44355, 7438, 300, 11, 1}, {1, 12, 566, 24103, 227968, 655702, 655702, 227968, 24103, 566, 12, 1}
%t Clear[t, p, x, n]; p[x_, n_] = (1 + x)^(n + 1) + If[n < 2, 0,x*((1 - x)^(n + 1)*PolyLog[ -n, x]/x + (1 + x)^(n - 1))/2]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, -1, 10}]; Flatten[%]
%K nonn
%O -1,5
%A _Roger L. Bagula_, Nov 06 2008