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A247376 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

%I A247376 #13 Oct 30 2014 18:30:13
%S A247376 1,2,2,3,5,5,15,8,8,35,33,13,80,131,48,21,171,409,279,34,355,1180,
%T A247376 1375,384,55,715,3128,5335,2895,89,1410,7858,18510,17029,3840,144,
%U A247376 2730,18851,58253,78609,35685,233,5208,43629,171059,317758,243873,46080,377,9810
%N A247376 Triangular array:  row n gives the coefficients of the polynomial p(n,x) defined in Comments.
%C A247376 The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = 1 + (2*x + 1)/f(n-1,x), where f(0,x) = 1.
%C A247376 (Sum of numbers in row n) = A059480(n+1) for n >= 0.
%C A247376 (Column 1) is essentially A000045 (Fibonacci numbers).
%H A247376 Clark Kimberling, <a href="/A247376/b247376.txt">Rows 0..100, flattened</a>
%F A247376 f(0,x) = 1/1, so that p(0,x) = 1
%F A247376 f(1,x) = (2 + 2 x)/1, so that p(1,x) = 2 + 2 x;
%F A247376 f(2,x) = (3 + 5 x)/(2 + 2 x), so that p(2,x) = 3 + 5 x.
%F A247376 First 6 rows of the triangle of coefficients:
%F A247376 1
%F A247376 2    2
%F A247376 3    5
%F A247376 5    15    8
%F A247376 8    35    33
%F A247376 13   80    131   48
%t A247376 z = 15; f[x_, n_] := 1 + (2 x + 1)/f[x, n - 1]; f[x_, 1] = 1;
%t A247376 t = Table[Factor[f[x, n]], {n, 1, z}]
%t A247376 u = Numerator[t]
%t A247376 TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A247376 array *)
%t A247376 Flatten[CoefficientList[u, x]] (* A247376 sequence *)
%o A247376 (PARI) rown(n) = if (n==0, 1, 1 + (2*x+1)/rown(n-1));
%o A247376 tabl(nn) = for (n=0, nn, print(Vecrev(numerator(rown(n))))); \\ _Michel Marcus_, Oct 28 2014
%Y A247376 Cf. A059480, A000045.
%K A247376 nonn,tabf,easy
%O A247376 0,2
%A A247376 _Clark Kimberling_, Oct 23 2014