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%I #7 Apr 23 2019 09:18:07
%S 1,1,1,1,4,1,1,7,7,1,1,16,14,16,1,1,37,34,34,37,1,1,86,111,52,111,86,
%T 1,1,199,341,163,163,341,199,1,1,456,988,696,198,696,988,456,1,1,1033,
%U 2724,2644,766,766,2644,2724,1033,1,1,2314,7213,9080,4050,764,4050,9080
%N Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n-2)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
%C Row sums are: {1, 2, 6, 16, 48, 144, 448, 1408, 4480, 14336, 46080}.
%e Triangle begins:
%e {1},
%e {1, 1},
%e {1, 4, 1},
%e {1, 7, 7, 1},
%e {1, 16, 14, 16, 1},
%e {1, 37, 34, 34, 37, 1},
%e {1, 86, 111, 52, 111, 86, 1},
%e {1, 199, 341, 163, 163, 341, 199, 1},
%e {1, 456, 988, 696, 198, 696, 988, 456, 1},
%e {1, 1033, 2724, 2644, 766, 766, 2644, 2724, 1033, 1},
%e {1, 2314, 7213, 9080, 4050, 764, 4050, 9080, 7213, 2314, 1}
%t p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n-2)*Sum[Binomial[n-m, 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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