A249138 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 6, 5, 7, 1, 1, 6, 18, 8, 10, 1, 1, 24, 26, 46, 12, 14, 1, 1, 24, 96, 58, 86, 16, 18, 1, 1, 120, 154, 326, 118, 156, 21, 23, 1, 1, 120, 600, 444, 756, 198, 246, 26, 28, 1, 1, 720, 1044, 2556, 1152, 1692, 324, 384, 32, 34, 1, 1

Offset

0,4

Comments

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + floor((n+1)/2))/f(n-1,x), where f(0,x) = 1. (Sum of numbers in row n) = A056952(n) for n >= 0. (Column 1) is essentially A091123 (repeated factorials).

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) = (2 + x + x^2)/(1 + x), so that p(2,x) = 2 + x + x^2).
First 6 rows of the triangle of coefficients:
1
1    1
2    1    1
2    4    1    1
6    5    7    1    1
6    18   8    10   1   1

Mathematica

z = 15; p[x_, n_] := x + Floor[(n+1)/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}]] (* A249138 array *)
Flatten[CoefficientList[u, x]] (* A249138 sequence *)

Crossrefs

Cf. A056952, A091123, A249128.

Sequence in context: A265005 A166288 A327001 * A056648 A056061 A029265

Adjacent sequences: A249135 A249136 A249137 * A249139 A249140 A249141

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Oct 22 2014

Status

approved