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%I #8 Oct 28 2014 00:09:33
%S 1,1,1,2,1,1,2,4,1,1,6,5,7,1,1,6,18,8,10,1,1,24,26,46,12,14,1,1,24,96,
%T 58,86,16,18,1,1,120,154,326,118,156,21,23,1,1,120,600,444,756,198,
%U 246,26,28,1,1,720,1044,2556,1152,1692,324,384,32,34,1,1
%N Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
%C The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + floor((n+1)/2))/f(n-1,x), where f(0,x) = 1. (Sum of numbers in row n) = A056952(n) for n >= 0. (Column 1) is essentially A091123 (repeated factorials).
%H Clark Kimberling, <a href="/A249138/b249138.txt">Rows 0..100, flattened</a>
%e f(0,x) = 1/1, so that p(0,x) = 1
%e f(1,x) = (1 + x)/1, so that p(1,x) = 1 + x;
%e f(2,x) = (2 + x + x^2)/(1 + x), so that p(2,x) = 2 + x + x^2).
%e First 6 rows of the triangle of coefficients:
%e 1
%e 1 1
%e 2 1 1
%e 2 4 1 1
%e 6 5 7 1 1
%e 6 18 8 10 1 1
%t z = 15; p[x_, n_] := x + Floor[(n+1)/2]/p[x, n - 1]; p[x_, 1] = 1;
%t t = Table[Factor[p[x, n]], {n, 1, z}]
%t u = Numerator[t]
%t TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249138 array *)
%t Flatten[CoefficientList[u, x]] (* A249138 sequence *)
%Y Cf. A056952, A091123, A249128.
%K nonn,tabl,easy
%O 0,4
%A _Clark Kimberling_, Oct 22 2014
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