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A249138 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 1
1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 6, 5, 7, 1, 1, 6, 18, 8, 10, 1, 1, 24, 26, 46, 12, 14, 1, 1, 24, 96, 58, 86, 16, 18, 1, 1, 120, 154, 326, 118, 156, 21, 23, 1, 1, 120, 600, 444, 756, 198, 246, 26, 28, 1, 1, 720, 1044, 2556, 1152, 1692, 324, 384, 32, 34, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + floor((n+1)/2))/f(n-1,x), where f(0,x) = 1.  (Sum of numbers in row n) = A056952(n) for n >= 0.  (Column 1) is essentially A091123 (repeated factorials).

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

First 6 rows of the triangle of coefficients:

1

1    1

2    1    1

2    4    1    1

6    5    7    1    1

6    18   8    10   1   1

MATHEMATICA

z = 15; p[x_, n_] := x + Floor[(n+1)/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}]] (* A249138 array *)

Flatten[CoefficientList[u, x]] (* A249138 sequence *)

CROSSREFS

Cf. A056952, A091123, A249128.

Sequence in context: A267998 A265005 A166288 * A056648 A056061 A029265

Adjacent sequences:  A249135 A249136 A249137 * A249139 A249140 A249141

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 22 2014

STATUS

approved

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Last modified April 20 08:50 EDT 2019. Contains 322306 sequences. (Running on oeis4.)