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%I #2 Mar 30 2012 17:34:27
%S 1,1,1,1,4,1,1,11,11,1,1,34,34,34,1,1,109,102,102,109,1,1,350,303,292,
%T 303,350,1,1,1127,901,819,819,901,1127,1,1,3688,2716,2296,2182,2296,
%U 2716,3688,1,1,12425,8420,6548,5822,5822,6548,8420,12425,1,1,43402
%N A polynomial based symmetrical sequence: p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(2^(m - 1) +n*m - n + 1)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}].
%C Row sums are:{1, 2, 6, 24, 104, 424, 1600, 5696, 19584, 66432, 226304}.
%F p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(2^(m - 1) +n*m - n + 1)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=Coefficients(p(x,m)).
%e {1}, {1, 1}, {1, 4, 1}, {1, 11, 11, 1}, {1, 34, 34, 34, 1}, {1, 109, 102, 102, 109, 1}, {1, 350, 303, 292, 303, 350, 1}, {1, 1127, 901, 819, 819, 901, 1127, 1}, {1, 3688, 2716, 2296, 2182, 2296, 2716, 3688, 1}, {1, 12425, 8420, 6548, 5822, 5822, 6548, 8420, 12425, 1}, {1, 43402, 27181, 19320, 15826, 14844, 15826, 19320, 27181, 43402, 1}
%t Clear[p, x, n]; p[x_, n_] = If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(2^(m - 1) + n*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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