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A249130 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 3
1, 2, 1, 2, 2, 1, 8, 6, 2, 1, 8, 16, 10, 2, 1, 48, 44, 28, 16, 2, 1, 48, 144, 104, 40, 22, 2, 1, 384, 400, 368, 232, 56, 30, 2, 1, 384, 1536, 1232, 688, 408, 72, 38, 2, 1, 3840, 4384, 5216, 3552, 1248, 708, 92, 48, 2, 1, 3840, 19200, 16704, 12096, 7632, 1968 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 2*floor(n/2))/f(n-1,x), where f(x,0) = 1.  (Sum of numbers in row n) = A249131(n) for n >= 0. (Column 1) = A037223.

LINKS

Clark Kimberling, Rows 0..100, flattened

EXAMPLE

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

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

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

First 6 rows of the triangle of coefficients:

1

2    1

2    2    1

8    6    2    1

8    16   10   2    1

48   44   28   16   2   1

MATHEMATICA

z = 15; p[x_, n_] := x + 2 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}]] (* A249130 array *)

Flatten[CoefficientList[u, x]] (* A249130 sequence *)

CROSSREFS

Cf. A249131, A037223, A249128.

Sequence in context: A273138 A181281 A171683 * A134997 A104605 A300953

Adjacent sequences:  A249127 A249128 A249129 * A249131 A249132 A249133

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 22 2014

STATUS

approved

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)