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A249252
Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
3
1, 1, 4, 1, 8, 8, 1, 12, 32, 16, 1, 16, 72, 96, 32, 1, 20, 128, 304, 256, 64, 1, 24, 200, 704, 1056, 640, 128, 1, 28, 288, 1360, 3072, 3264, 1536, 256, 1, 32, 392, 2336, 7200, 11520, 9344, 3584, 512, 1, 36, 512, 3696, 14592, 32064, 38912, 25344, 8192, 1024
OFFSET
0,3
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = 2*x + 1 + 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) = (1 + 4 x)/1, so that p(1,x) = 1 + 4 x;
f(2,x) = (1 + 8 x + 8 x^2)/(1 + 4 x), so that p(2,x) = 1 + 8 x + 8 x^2.
First 6 rows of the triangle of coefficients:
1
1 4
1 8 8
1 12 32 16
1 16 72 96 32
1 20 128 304 256 64
MATHEMATICA
z = 14; f[n_, x_] := 2 x + 1 + 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}]]] (* A249252 array *)
v = Flatten[CoefficientList[u, x]] (* A249252 sequence *)
CROSSREFS
Sequence in context: A335707 A232816 A210196 * A128414 A192014 A019699
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Oct 24 2014
STATUS
approved