A249252 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

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

Cf. A249250, A249251.

Sequence in context: A335707 A232816 A210196 * A128414 A192014 A019699

Adjacent sequences: A249249 A249250 A249251 * A249253 A249254 A249255

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Oct 24 2014

Status

approved