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A249100 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 2
1, 3, 1, 5, 3, 1, 21, 12, 3, 1, 45, 48, 21, 3, 1, 231, 177, 81, 32, 3, 1, 585, 855, 450, 120, 45, 3, 1, 3465, 3240, 2070, 930, 165, 60, 3, 1, 9945, 18000, 10890, 4110, 1695, 216, 77, 3, 1, 65835, 71505, 57330, 28560, 7245, 2835, 273, 96, 3, 1, 208845, 443835 (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*n - 1)/f(n-1,x), where f(0,x) = 1.  (Sum of numbers in row n) = A249101(n) for n >= 0.  (n-th term of column 1) = A235136(n) for n >= 1.

LINKS

Clark Kimberling, Rows 0..100, flattened

EXAMPLE

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

f(1,x) = (3 + x)/1, so that p(1,x) = 3 + x;

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

First 6 rows of the triangle of coefficients:

1

3    1

5    3    1

21   12   3    1

45   48   21   3    1

231  177  81   32   3   1

MATHEMATICA

z = 11; p[x_, n_] := x + (2 n - 1)/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}]] (* A249100 array *)

Flatten[CoefficientList[u, x]] (* A249100 sequence  *)

v = u /. x -> 1  (* A249101 *)

u /. x -> 0  (* A235136 *)

CROSSREFS

Cf. A249101, A245136, A087299.

Sequence in context: A135224 A209578 A268829 * A152203 A161946 A013597

Adjacent sequences:  A249097 A249098 A249099 * A249101 A249102 A249103

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 21 2014

STATUS

approved

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Last modified August 16 13:28 EDT 2017. Contains 290623 sequences.