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%I #11 Aug 03 2019 05:17:38
%S 1,1,1,1,4,1,1,5,5,1,1,7,8,7,1,1,9,13,13,9,1,1,11,21,22,21,11,1,1,13,
%T 31,39,39,31,13,1,1,15,43,66,72,66,43,15,1,1,17,57,104,131,131,104,57,
%U 17,1,1,19,73,155,225,254,225,155,73,19,1
%N Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[Binomial[n-m, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
%C Row sums are: {1, 2, 6, 12, 24, 46, 88, 168, 322, 620, 1200}.
%e Triangle begins:
%e {1},
%e {1, 1},
%e {1, 4, 1},
%e {1, 5, 5, 1},
%e {1, 7, 8, 7, 1},
%e {1, 9, 13, 13, 9, 1},
%e {1, 11, 21, 22, 21, 11, 1},
%e {1, 13, 31, 39, 39, 31, 13, 1},
%e {1, 15, 43, 66, 72, 66, 43, 15, 1},
%e {1, 17, 57, 104, 131, 131, 104, 57, 17, 1},
%e {1, 19, 73, 155, 225, 254, 225, 155, 73, 19, 1}
%t p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 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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