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A249250 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 4
1, 1, 3, 1, 6, 3, 1, 9, 15, 3, 1, 12, 36, 24, 3, 1, 15, 66, 90, 33, 3, 1, 18, 105, 228, 171, 42, 3, 1, 21, 153, 465, 579, 279, 51, 3, 1, 24, 210, 828, 1500, 1200, 414, 60, 3, 1, 27, 276, 1344, 3258, 3858, 2172, 576, 69, 3, 1, 30, 351, 2040, 6258, 10116, 8430 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The polynomial p(n,x) is given by p(n,x) = (x + 1)*p(n-1,x) + 2x, where p(0,x) = 1.

LINKS

Clark Kimberling, Rows 0..100, flattened

EXAMPLE

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

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

f(2,x) = (1 + 6 x + 3 x^2)/(1 + 3 x), so that p(2,x) = 1 + 6 x + 3 x^2.

First 6 rows of the triangle of coefficients:

1

1      3

1      6      3

1      9      15       3

1      12     36       24     3

1      15     66       90     33    3

MATHEMATICA

z = 14; f[x_, n_] := x + 1 + 2 x/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}]] (* A249250 array *)

Flatten[CoefficientList[u, x]] (* A249250 sequence *)

PROG

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

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

CROSSREFS

Cf. A249247.

Sequence in context: A145366 A145367 A124928 * A122432 A131110 A133093

Adjacent sequences:  A249247 A249248 A249249 * A249251 A249252 A249253

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Oct 24 2014

STATUS

approved

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