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

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

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