%I A158208
%S A158208 2,1,1,1,0,1,2,3,3,2,3,4,0,4,3,6,15,10,10,15,6,10,24,15,0,15,24,
%T A158208 10,20,70,84,35,35,84,70,20,35,120,140,56,0,56,140,120,35,70,
%U A158208 315,540,420,126,126,420,540,315,70,126,560,945,720,210,0,210
%V A158208 2,1,1,1,0,1,-2,3,3,-2,-3,4,0,4,-3,6,-15,10,10,-15,6,10,-24,15,0,15,-24,
%W A158208 10,-20,70,-84,35,35,-84,70,-20,-35,120,-140,56,0,56,-140,120,-35,70,
%X A158208 -315,540,-420,126,126,-420,540,-315,70,126,-560,945,-720,210,0,210
%N A158208 A symmetrical triangle of polynomial coefficients: p(x,n)=If[n == 0, 
               2, Sum[Binomial[n, i]*(x - 1)^i, {i, 0, Floor[(n - 1)/2]}] + x^n*Sum[ 
               Binomial[n, i]*(1/x - 1)^i, {i, 0, Floor[(n - 1)/2]}]].
%C A158208 Straight row sums are two, but absolute value row sums are:
%C A158208 {2, 2, 2, 10, 14, 62, 98, 418, 702, 2942, 5122,...}.
%F A158208 p(x,n)=If[n == 0, 2, Sum[Binomial[n, i]*(x - 1)^i, {i, 0, Floor[(n - 
               1)/2]}] + x^n*Sum[ Binomial[n, i]*(1/x - 1)^i, {i, 0, Floor[(n - 
               1)/2]}]];
%F A158208 out(n,m)=coefficients(p(x,n)).
%e A158208 {2},
%e A158208 {1, 1},
%e A158208 {1, 0, 1},
%e A158208 {-2, 3, 3, -2},
%e A158208 {-3, 4, 0, 4, -3},
%e A158208 {6, -15, 10, 10, -15, 6},
%e A158208 {10, -24, 15, 0, 15, -24, 10},
%e A158208 {-20, 70, -84, 35, 35, -84, 70, -20},
%e A158208 {-35, 120, -140, 56, 0, 56, -140, 120, -35},
%e A158208 {70, -315, 540, -420, 126, 126, -420, 540, -315, 70},
%e A158208 {126, -560, 945, -720, 210, 0, 210, -720, 945, -560, 126}
%t A158208 Clear[p, x, n];
%t A158208 p[x_, n_] = If[ n == 0, 2, Sum[Binomial[ n, i]*(x - 1)^i, {i, 0, Floor[(n 
               - 1)/2]}] + Expand[x^n*Sum[Binomial[n, i]*(1/x - 1)^ i, {i, 0, Floor[(n 
               - 1)/2]}]]];
%t A158208 Table[CoefficientList[p[x, n], x], {n, 0, 10}];
%t A158208 Flatten[%]
%Y A158208 Sequence in context: A093718 A035212 A068029 this_sequence A117274 A140883 
               A064744
%Y A158208 Adjacent sequences: A158205 A158206 A158207 this_sequence A158209 A158210 
               A158211
%K A158208 sign,tabl,uned
%O A158208 0,1
%A A158208 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 13 2009