%I #7 Apr 23 2019 09:18:30

%S 1,1,1,1,6,1,1,15,15,1,1,36,54,36,1,1,85,170,170,85,1,1,198,495,660,

%T 495,198,1,1,455,1365,2275,2275,1365,455,1,1,1032,3612,7224,9030,7224,

%U 3612,1032,1,1,2313,9252,21588,32382,32382,21588,9252,2313,1,1,5130,23085

%N Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 2)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

%C Row sums are: {1, 2, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288}.

%e Triangle begins:

%e {1},

%e {1, 1},

%e {1, 6, 1},

%e {1, 15, 15, 1},

%e {1, 36, 54, 36, 1},

%e {1, 85, 170, 170, 85, 1},

%e {1, 198, 495, 660, 495, 198, 1},

%e {1, 455, 1365, 2275, 2275, 1365, 455, 1},

%e {1, 1032, 3612, 7224, 9030, 7224, 3612, 1032, 1},

%e {1, 2313, 9252, 21588, 32382, 32382, 21588, 9252, 2313, 1},

%e {1, 5130, 23085, 61560, 107730, 129276, 107730, 61560, 23085, 5130, 1}

%t Cp[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 2)*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