A249159 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

1, 1, 1, 3, 2, 2, 4, 7, 2, 2, 15, 18, 24, 4, 4, 24, 57, 30, 36, 4, 4, 105, 174, 282, 88, 100, 8, 8, 192, 561, 414, 570, 120, 132, 8, 8, 945, 1950, 3660, 1620, 2040, 312, 336, 16, 16, 1920, 6555, 6090, 9360, 2820, 3360, 392, 416, 16, 16, 10395, 25290, 53370

Offset

0,4

Comments

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = 1 + n)/(2*f(n-1,x)), where f(0,x) = 1.

(Sum of numbers in row n) = A000982(n+1) for n >= 0.

Column 1 is essentially A081405.

Links

Clark Kimberling, Rows 0..100, flattened

Formula

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

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

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

First 6 rows of the triangle of coefficients:

1

1 1

3 2 2

4 7 2 2

15 18 24 4 4

24 57 30 36 4 4

Mathematica

z = 15; f[x_, n_] := 1 + n/(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}]] (* A249159 array *)
Flatten[CoefficientList[u, x]] (* A249159 sequence *)

Crossrefs

Cf. A000982, A081405.

Sequence in context: A344985 A325596 A254876 * A230871 A111241 A345055

Adjacent sequences: A249156 A249157 A249158 * A249160 A249161 A249162

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Oct 23 2014

Status

approved