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A247376 Triangular array:  row n gives the coefficients of the polynomial p(n,x) defined in Comments. 1
1, 2, 2, 3, 5, 5, 15, 8, 8, 35, 33, 13, 80, 131, 48, 21, 171, 409, 279, 34, 355, 1180, 1375, 384, 55, 715, 3128, 5335, 2895, 89, 1410, 7858, 18510, 17029, 3840, 144, 2730, 18851, 58253, 78609, 35685, 233, 5208, 43629, 171059, 317758, 243873, 46080, 377, 9810 (list; 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) = 1 + (2*x + 1)/f(n-1,x), where f(0,x) = 1.

(Sum of numbers in row n) = A059480(n+1) for n >= 0.

(Column 1) is essentially A000045 (Fibonacci numbers).

LINKS

Clark Kimberling, Rows 0..100, flattened

FORMULA

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

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

f(2,x) = (3 + 5 x)/(2 + 2 x), so that p(2,x) = 3 + 5 x.

First 6 rows of the triangle of coefficients:

1

2    2

3    5

5    15    8

8    35    33

13   80    131   48

MATHEMATICA

z = 15; f[x_, n_] := 1 + (2 x + 1)/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}]] (* A247376 array *)

Flatten[CoefficientList[u, x]] (* A247376 sequence *)

PROG

(PARI) rown(n) = if (n==0, 1, 1 + (2*x+1)/rown(n-1));

tabl(nn) = for (n=0, nn, print(Vecrev(numerator(rown(n))))); \\ Michel Marcus, Oct 28 2014

CROSSREFS

Cf. A059480, A000045.

Sequence in context: A035537 A285407 A292802 * A101779 A169891 A137756

Adjacent sequences:  A247373 A247374 A247375 * A247377 A247378 A247379

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Oct 23 2014

STATUS

approved

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Last modified June 25 05:41 EDT 2019. Contains 324346 sequences. (Running on oeis4.)