A249139 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

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

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