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A249159 Triangular array:  row n gives the coefficients of the polynomial p(n,x) defined in Comments. 2

%I

%S 1,1,1,3,2,2,4,7,2,2,15,18,24,4,4,24,57,30,36,4,4,105,174,282,88,100,

%T 8,8,192,561,414,570,120,132,8,8,945,1950,3660,1620,2040,312,336,16,

%U 16,1920,6555,6090,9360,2820,3360,392,416,16,16,10395,25290,53370

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

%C (Sum of numbers in row n) = A000982(n+1) for n >= 0.

%C Column 1 is essentially A081405.

%H Clark Kimberling, <a href="/A249159/b249159.txt">Rows 0..100, flattened</a>

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

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

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

%F First 6 rows of the triangle of coefficients:

%F 1

%F 1 1

%F 3 2 2

%F 4 7 2 2

%F 15 18 24 4 4

%F 24 57 30 36 4 4

%t z = 15; f[x_, n_] := 1 + n/(2 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}]] (* A249159 array *)

%t Flatten[CoefficientList[u, x]] (* A249159 sequence *)

%Y Cf. A000982, A081405.

%K nonn,tabl,easy

%O 0,4

%A _Clark Kimberling_, Oct 23 2014

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Last modified June 17 13:59 EDT 2021. Contains 345083 sequences. (Running on oeis4.)