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Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
1

%I #13 Oct 30 2014 18:30:13

%S 1,2,2,3,5,5,15,8,8,35,33,13,80,131,48,21,171,409,279,34,355,1180,

%T 1375,384,55,715,3128,5335,2895,89,1410,7858,18510,17029,3840,144,

%U 2730,18851,58253,78609,35685,233,5208,43629,171059,317758,243873,46080,377,9810

%N Triangular array: 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) = 1 + (2*x + 1)/f(n-1,x), where f(0,x) = 1.

%C (Sum of numbers in row n) = A059480(n+1) for n >= 0.

%C (Column 1) is essentially A000045 (Fibonacci numbers).

%H Clark Kimberling, <a href="/A247376/b247376.txt">Rows 0..100, flattened</a>

%F f(0,x) = 1/1, so that p(0,x) = 1

%F f(1,x) = (2 + 2 x)/1, so that p(1,x) = 2 + 2 x;

%F f(2,x) = (3 + 5 x)/(2 + 2 x), so that p(2,x) = 3 + 5 x.

%F First 6 rows of the triangle of coefficients:

%F 1

%F 2 2

%F 3 5

%F 5 15 8

%F 8 35 33

%F 13 80 131 48

%t z = 15; f[x_, n_] := 1 + (2 x + 1)/f[x, n - 1]; f[x_, 1] = 1;

%t t = Table[Factor[f[x, n]], {n, 1, z}]

%t u = Numerator[t]

%t TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A247376 array *)

%t Flatten[CoefficientList[u, x]] (* A247376 sequence *)

%o (PARI) rown(n) = if (n==0, 1, 1 + (2*x+1)/rown(n-1));

%o tabl(nn) = for (n=0, nn, print(Vecrev(numerator(rown(n))))); \\ _Michel Marcus_, Oct 28 2014

%Y Cf. A059480, A000045.

%K nonn,tabf,easy

%O 0,2

%A _Clark Kimberling_, Oct 23 2014