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%I #8 Apr 23 2019 09:18:23
%S 1,1,1,1,4,1,1,9,9,1,1,20,30,20,1,1,45,90,90,45,1,1,102,255,340,255,
%T 102,1,1,231,693,1155,1155,693,231,1,1,520,1820,3640,4550,3640,1820,
%U 520,1,1,1161,4644,10836,16254,16254,10836,4644,1161,1,1,2570,11565,30840,53970
%N Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
%C Row sums are: {1, 2, 6, 20, 72, 272, 1056, 4160, 16512, 65792, 262656}.
%e Triangle begins:
%e {1},
%e {1, 1},
%e {1, 4, 1},
%e {1, 9, 9, 1},
%e {1, 20, 30, 20, 1},
%e {1, 45, 90, 90, 45, 1},
%e {1, 102, 255, 340, 255, 102, 1},
%e {1, 231, 693, 1155, 1155, 693, 231, 1},
%e {1, 520, 1820, 3640, 4550, 3640, 1820, 520, 1},
%e {1, 1161, 4644, 10836, 16254, 16254, 10836, 4644, 1161, 1},
%e {1, 2570, 11565, 30840, 53970, 64764, 53970, 30840, 11565, 2570, 1}
%t p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]];
%t Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]
%K nonn,tabl,less
%O 0,5
%A _Roger L. Bagula_, Nov 02 2008
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