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A249128 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 3
1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 6, 11, 7, 8, 1, 1, 6, 18, 26, 10, 11, 1, 1, 24, 50, 46, 58, 14, 15, 1, 1, 24, 96, 154, 86, 102, 18, 19, 1, 1, 120, 274, 326, 444, 156, 177, 23, 24, 1, 1, 120, 600, 1044, 756, 954, 246, 272, 28, 29, 1, 1, 720, 1764 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + floor(n/2))/f(n-1,x), where f(x,0) = 1.  (Sum of numbers in row n) = A056953(n) for n >= 0. Column 1 consists of repeated factorials (A000142), as in A081123.

LINKS

Clark Kimberling, Rows 0..100, flattened

EXAMPLE

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

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

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

First 6 rows of the triangle of coefficients:

1

1    1

1    1    1

2    3    1    1

2    4    5    1    1

6    11   7    8    1   1

MATHEMATICA

z = 15; p[x_, n_] := x + Floor[n/2]/p[x, n - 1]; p[x_, 1] = 1;

t = Table[Factor[p[x, n]], {n, 1, z}]

u = Numerator[t]

TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249128 array *)

Flatten[CoefficientList[u, x]] (* A249128 sequence *)

CROSSREFS

Cf. A056953, A000142, A081123, A249130.

Sequence in context: A114732 A123338 A152735 * A046226 A054722 A256187

Adjacent sequences:  A249125 A249126 A249127 * A249129 A249130 A249131

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 22 2014

STATUS

approved

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Last modified June 28 03:23 EDT 2017. Contains 288813 sequences.