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%I #8 Apr 24 2019 06:12:08
%S 1,1,1,1,18,1,1,35,35,1,1,100,70,100,1,1,261,202,202,261,1,1,646,783,
%T 276,783,646,1,1,1543,2581,1059,1059,2581,1543,1,1,3592,7708,5176,
%U 1094,5176,7708,3592,1,1,8201,21540,20564,5246,5246,20564,21540,8201,1,1
%N Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n+1)*Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
%C Row sums are: {1, 2, 20, 72, 272, 928, 3136, 10368, 34048, 111104, 361472}.
%e Triangle begins:
%e {1},
%e {1, 1},
%e {1, 18, 1},
%e {1, 35, 35, 1},
%e {1, 100, 70, 100, 1},
%e {1, 261, 202, 202, 261, 1},
%e {1, 646, 783, 276, 783, 646, 1},
%e {1, 1543, 2581, 1059, 1059, 2581, 1543, 1},
%e {1, 3592, 7708, 5176, 1094, 5176, 7708, 3592, 1},
%e {1, 8201, 21540, 20564, 5246, 5246, 20564, 21540, 8201, 1},
%e {1, 18442, 57389, 71800, 30930, 4348, 30930, 71800, 57389, 18442, 1}
%t p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n+1)*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