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A249057 Triangular array:  Row n shows the coefficients of polynomials p(n,x) defined in Comments. 5
1, 4, 1, 5, 4, 1, 24, 11, 4, 1, 35, 52, 18, 4, 1, 192, 123, 84, 26, 4, 1, 315, 660, 285, 120, 35, 4, 1, 1920, 1545, 1500, 545, 160, 45, 4, 1, 3465, 9180, 4680, 2820, 930, 204, 56, 4, 1, 23040, 22005, 27180, 11220, 4740, 1470, 252, 68, 4, 1, 45045, 142380 (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 + (n + 1)/f(n-1,x), where f(x,0) = 1.

Row sums give A249059(n) for n >= 1.

First column is A249060 (n-th term = n!! for n >= 0).

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..5049

EXAMPLE

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

f(1,x) = (4 + x)/1, so that p(1,x) = 4 + x;

f(2,x) = (5 + 4 x + x^2)/(1 + x), so that p(2,x) = 5 + 4 x + x^2.

First 6 rows of the triangle of coefficients:

1

4    1

5    4     1

24   11    4    1

35   52    18   4    1

192  123   84   26   4   1

MATHEMATICA

z = 12; f[x_, n_] := x + (n+2)/f[x, n - 1];

f[x_, 0] = 1; t = Table[Factor[f[x, n]], {n, 0, z}];

u = Numerator[t]; TableForm[Rest[Table[CoefficientList[u[[n]], x], {n, 0, z}]]]

Flatten[CoefficientList[u, x]] (* A249057 sequence *)

CROSSREFS

Cf. A249059, A249060.

Sequence in context: A030352 A212643 A104571 * A105721 A099310 A021880

Adjacent sequences:  A249054 A249055 A249056 * A249058 A249059 A249060

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 20 2014

STATUS

approved

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Last modified April 29 22:12 EDT 2017. Contains 285615 sequences.