A249130 Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

1, 2, 1, 2, 2, 1, 8, 6, 2, 1, 8, 16, 10, 2, 1, 48, 44, 28, 16, 2, 1, 48, 144, 104, 40, 22, 2, 1, 384, 400, 368, 232, 56, 30, 2, 1, 384, 1536, 1232, 688, 408, 72, 38, 2, 1, 3840, 4384, 5216, 3552, 1248, 708, 92, 48, 2, 1, 3840, 19200, 16704, 12096, 7632, 1968, 1088, 112, 58, 2, 1

Offset

0,2

Comments

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

(Sum of numbers in row n) = A249131(n) for n >= 0.

(Column 1) = A037223.

Links

Clark Kimberling, Rows 0..100, flattened

Example

f(0,x) = 1/1, so that p(0,x) = 1;
f(1,x) = (2 + x)/1, so that p(1,x) = 2 + x;
f(2,x) = (2 + 2*x + x^2)/(3 + x), so that p(2,x) = 2 + 2*x + x^2.
First 6 rows of the triangle of coefficients:
  1
  2    1
  2    2    1
  8    6    2    1
  8    16   10   2    1
  48   44   28   16   2   1

Mathematica

z = 15; p[x_, n_] := x + 2 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}]] (* A249130 array *)
Flatten[CoefficientList[u, x]] (* A249130 sequence *)

Crossrefs

Cf. A249131, A037223, A249128.

Sequence in context: A273138 A181281 A171683 * A134997 A355691 A337474

Adjacent sequences: A249127 A249128 A249129 * A249131 A249132 A249133

Keyword

nonn,tabl,easy,changed

Author

Clark Kimberling, Oct 22 2014

Status

approved