A249128 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 6, 11, 7, 8, 1, 1, 6, 18, 26, 10, 11, 1, 1, 24, 50, 46, 58, 14, 15, 1, 1, 24, 96, 154, 86, 102, 18, 19, 1, 1, 120, 274, 326, 444, 156, 177, 23, 24, 1, 1, 120, 600, 1044, 756, 954, 246, 272, 28, 29, 1, 1, 720, 1764

Offset

0,7

Comments

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + floor(n/2))/f(n-1,x), where f(x,0) = 1. (Sum of numbers in row n) = A056953(n) for n >= 0. Column 1 consists of repeated factorials (A000142), as in A081123.

Links

Clark Kimberling, Rows 0..100, flattened

Example

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) = (1 + x + x^2)/(1 + x), so that p(2,x) = 1 + x + x^2).
First 6 rows of the triangle of coefficients:
1
1    1
1    1    1
2    3    1    1
2    4    5    1    1
6    11   7    8    1   1

Mathematica

z = 15; p[x_, n_] := x + Floor[n/2]/p[x, n - 1]; p[x_, 1] = 1;
t = Table[Factor[p[x, n]], {n, 1, z}]
u = Numerator[t]
TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249128 array *)
Flatten[CoefficientList[u, x]] (* A249128 sequence *)

Crossrefs

Cf. A056953, A000142, A081123, A249130.

Sequence in context: A114732 A123338 A152735 * A299481 A304738 A046226

Adjacent sequences: A249125 A249126 A249127 * A249129 A249130 A249131

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Oct 22 2014

Status

approved