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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
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
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Oct 24 2014
STATUS
approved