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%I #2 Mar 30 2012 17:34:27
%S 1,1,1,1,6,1,1,15,15,1,1,44,38,44,1,1,165,106,106,165,1,1,774,367,276,
%T 367,774,1,1,4167,1621,867,867,1621,4167,1,1,23944,8476,3512,2374,
%U 3512,8476,23944,1,1,141321,48164,17492,8318,8318,17492,48164,141321,1,1
%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+1 )*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
%C Row sums are:{1, 2, 8, 32, 128, 544, 2560, 13312, 74240, 430592, 2545664}.
%F p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(3^(m-1) + 2*m+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, 15, 15, 1}, {1, 44, 38, 44, 1}, {1, 165, 106, 106, 165, 1}, {1, 774, 367, 276, 367, 774, 1}, {1, 4167, 1621, 867, 867, 1621, 4167, 1}, {1, 23944, 8476, 3512, 2374, 3512, 8476, 23944, 1}, {1, 141321, 48164, 17492, 8318, 8318, 17492, 48164, 141321, 1}, {1, 842762, 283181, 97400, 37586, 23804, 37586, 97400, 283181, 842762, 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+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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