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A249139 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

%I A249139 #6 Oct 28 2014 00:10:41
%S A249139 1,3,1,5,2,11,7,1,21,16,3,43,41,12,1,85,94,34,4,171,219,99,18,1,341,
%T A249139 492,261,60,5,683,1101,678,195,25,1,1365,2426,1692,576,95,6,2731,5311,
%U A249139 4149,1644,340,33,1,5461,11528,9959,4488,1106,140,7,10923,24881
%N A249139 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
%C A249139 The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = 1 + (x + 2)/f(n-1,x), where f(0,x) = 1.
%C A249139 (Sum of numbers in row n) = A006130(n+1) for n >= 0.
%C A249139 (Column 1) is essentially A001045.
%H A249139 Clark Kimberling, <a href="/A249139/b249139.txt">Rows 0..100, flattened</a>
%e A249139 f(0,x) = 1/1, so that p(0,x) = 1
%e A249139 f(1,x) = (3 + x)/1, so that p(1,x) = 3 + x;
%e A249139 f(2,x) = (5 + 2 x)/(3 + x), so that p(2,x) = 5 + 2 x.
%e A249139 First 6 rows of the triangle of coefficients:
%e A249139 1
%e A249139 3    1
%e A249139 5    2
%e A249139 11   7    1
%e A249139 21   16   3
%e A249139 43   41   12  1
%t A249139 z = 15; f[x_, n_] := 1 + (x + 2)/f[x, n - 1]; f[x_, 1] = 1;
%t A249139 t = Table[Factor[f[x, n]], {n, 1, z}]
%t A249139 u = Numerator[t]
%t A249139 TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249139 array *)
%t A249139 Flatten[CoefficientList[u, x]] (* A249139 sequence *)
%Y A249139 Cf. A006130, A001045.
%K A249139 nonn,tabf,easy
%O A249139 0,2
%A A249139 _Clark Kimberling_, Oct 23 2014