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%I #2 Mar 30 2012 17:34:27
%S 1,1,1,1,6,1,1,17,17,1,1,52,46,52,1,1,189,130,130,189,1,1,838,431,340,
%T 431,838,1,1,4327,1781,1027,1027,1781,4327,1,1,24328,8860,3896,2758,
%U 3896,8860,24328,1,1,142217,49060,18388,9214,9214,18388,49060,142217,1
%N A functionally symmetric Polynomial as a triangle of coefficients: p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(3^(m-1) + 2*m+(n-1) )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
%C Row sums are:{1, 2, 8, 36, 152, 640, 2880, 14272, 76928, 437760, 2564096}.
%F p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(3^(m-1) + 2*m+(n-1) )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).
%e {1}, {1, 1}, {1, 6, 1}, {1, 17, 17, 1}, {1, 52, 46, 52, 1}, {1, 189, 130, 130, 189, 1}, {1, 838, 431, 340, 431, 838, 1}, {1, 4327, 1781, 1027, 1027, 1781, 4327, 1}, {1, 24328, 8860, 3896, 2758, 3896, 8860, 24328, 1}, {1, 142217, 49060, 18388, 9214, 9214, 18388, 49060, 142217, 1}, {1, 844810, 285229, 99448, 39634, 25852, 39634, 99448, 285229, 844810, 1}
%t Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(3^(m-1) + 2*m+(n-1) )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]
%K nonn
%O 0,5
%A _Roger L. Bagula_, Nov 03 2008
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