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A249253 Triangular array:  row n gives the coefficients of the polynomial p(n,x) defined in Comments. 1
1, 3, 1, 12, 5, 60, 28, 1, 360, 180, 11, 2520, 1320, 105, 1, 20160, 10920, 1020, 19, 181440, 100800, 10500, 276, 1, 1814400, 1028160, 115920, 3780, 29, 19958400, 11491200, 1375920, 52080, 595, 1, 239500800, 139708800, 17539200, 740880, 10920, 41, 3113510400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

Clark Kimberling, Rows 0..100, flattened

EXAMPLE

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

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

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

First 6 rows of the triangle of coefficients:

1

3     1

12    5

60    28     1

360   180    11

2520  1320   105    1

MATHEMATICA

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

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

u = Numerator[t]

TableForm[Rest[Table[CoefficientList[u[[n]], x], {n, 0, z}]]] (* A249253 array *)

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

CROSSREFS

Cf. A249250, A249251, A249252.

Sequence in context: A185105 A122844 A113369 * A201638 A127894 A127898

Adjacent sequences:  A249250 A249251 A249252 * A249254 A249255 A249256

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Oct 24 2014

STATUS

approved

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Last modified June 20 02:51 EDT 2021. Contains 345157 sequences. (Running on oeis4.)