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A249139 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 1
1, 3, 1, 5, 2, 11, 7, 1, 21, 16, 3, 43, 41, 12, 1, 85, 94, 34, 4, 171, 219, 99, 18, 1, 341, 492, 261, 60, 5, 683, 1101, 678, 195, 25, 1, 1365, 2426, 1692, 576, 95, 6, 2731, 5311, 4149, 1644, 340, 33, 1, 5461, 11528, 9959, 4488, 1106, 140, 7, 10923, 24881 (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 + (x + 2)/f(n-1,x), where f(0,x) = 1.

(Sum of numbers in row n) = A006130(n+1) for n >= 0.

(Column 1) is essentially A001045.

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

First 6 rows of the triangle of coefficients:

1

3    1

5    2

11   7    1

21   16   3

43   41   12  1

MATHEMATICA

z = 15; f[x_, n_] := 1 + (x + 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}]] (* A249139 array *)

Flatten[CoefficientList[u, x]] (* A249139 sequence *)

CROSSREFS

Cf. A006130, A001045.

Sequence in context: A065168 A318581 A065277 * A059971 A184343 A099548

Adjacent sequences:  A249136 A249137 A249138 * A249140 A249141 A249142

KEYWORD

nonn,tabf,easy

AUTHOR

Clark Kimberling, Oct 23 2014

STATUS

approved

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)