A249250 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

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

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