A249251 - OEIS

%I #7 Nov 09 2014 00:11:50

%S 1,1,3,1,6,6,1,9,21,12,1,12,45,60,24,1,15,78,171,156,48,1,18,120,372,

%T 558,384,96,1,21,171,690,1473,1656,912,192,1,24,231,1152,3225,5160,

%U 4608,2112,384,1,27,300,1785,6219,13083,16584,12240,4800,768,1,30

%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) = 2 x + 1 + x/f(n-1,x), where f(0,x) = 1.

%H Clark Kimberling, <a href="/A249251/b249251.txt">Table of n, a(n) for n = 0..5150</a>

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

%e f(1,x) = (1 + 3 x)/1, so that p(1,x) = 1 + 3 x;

%e f(2,x) = (1 + 6 x + 3 x^2)/(1 + 3 x), so that p(2,x) = 1 + 6 x + 3 x^2.

%e First 6 rows of the triangle of coefficients:

%e 1

%e 1      3

%e 1      6      6

%e 1      9      21       12

%e 1      12     45       60     24

%e 1      15     78       171    156    48

%t z = 14; f[n_, x_] := 2 x + 1 + x/f[n - 1, x]; f[0, x_] = 1;

%t t = Table[Factor[f[n, x]], {n, 0, z}]

%t u = Numerator[t]

%t TableForm[Rest[Table[CoefficientList[u[[n]], x], {n, 0, z}]]] (*A249251 array*)

%t Flatten[CoefficientList[u, x]] (*A249251 sequence*)

%Y Cf. A249247, A249248, A249250, A249252.

%K nonn,tabl,easy

%O 0,3

%A _Clark Kimberling_, Oct 24 2014