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A249253 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 1

%I #7 Jan 09 2015 14:22:45

%S 1,3,1,12,5,60,28,1,360,180,11,2520,1320,105,1,20160,10920,1020,19,

%T 181440,100800,10500,276,1,1814400,1028160,115920,3780,29,19958400,

%U 11491200,1375920,52080,595,1,239500800,139708800,17539200,740880,10920,41,3113510400

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

%H Clark Kimberling, <a href="/A249253/b249253.txt">Rows 0..100, flattened</a>

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

%e f(1,x) = (12 + 5 x)/1, so that p(1,x) = 12 + 5 x;

%e f(2,x) = (60 + 28 x + x^2)/(1 + 4 x), so that p(2,x) = 60 + 28 x + x^2.

%e First 6 rows of the triangle of coefficients:

%e 1

%e 3 1

%e 12 5

%e 60 28 1

%e 360 180 11

%e 2520 1320 105 1

%t z = 14; f[n_, x_] := n + 2 + 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}]]] (* A249253 array *)

%t Flatten[CoefficientList[u, x]] (* A249253 sequence *)

%Y Cf. A249250, A249251, A249252.

%K nonn,tabf,easy

%O 0,2

%A _Clark Kimberling_, Oct 24 2014

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)