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A249159 Triangular array:  row n gives the coefficients of the polynomial p(n,x) defined in Comments. 2
1, 1, 1, 3, 2, 2, 4, 7, 2, 2, 15, 18, 24, 4, 4, 24, 57, 30, 36, 4, 4, 105, 174, 282, 88, 100, 8, 8, 192, 561, 414, 570, 120, 132, 8, 8, 945, 1950, 3660, 1620, 2040, 312, 336, 16, 16, 1920, 6555, 6090, 9360, 2820, 3360, 392, 416, 16, 16, 10395, 25290, 53370 (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) = 1 + n)/(2*f(n-1,x)), where f(0,x) = 1.

(Sum of numbers in row n) = A000982(n+1) for n >= 0.

Column 1 is essentially A081405.

LINKS

Clark Kimberling, Rows 0..100, flattened

FORMULA

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) = (3 + 2 x + x^2)/(1 + x), so that p(2,x) = 3 + 2 x + x^2.

First 6 rows of the triangle of coefficients:

1

1    1

3    2     2

4    7     2     2

15   18    24    4     4

24   57    30    36    4    4

MATHEMATICA

z = 15; f[x_, n_] := 1 + n/(2 f[x, n - 1]); f[x_, 1] = 1;

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

u = Numerator[t]

TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249159 array *)

Flatten[CoefficientList[u, x]] (* A249159 sequence *)

CROSSREFS

Cf. A000982, A081405.

Sequence in context: A245572 A325596 A254876 * A230871 A111241 A247501

Adjacent sequences:  A249156 A249157 A249158 * A249160 A249161 A249162

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 23 2014

STATUS

approved

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Last modified August 7 17:02 EDT 2020. Contains 336277 sequences. (Running on oeis4.)