A249074 Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.

1, 4, 1, 6, 4, 1, 32, 14, 4, 1, 60, 72, 24, 4, 1, 384, 228, 120, 36, 4, 1, 840, 1392, 564, 176, 50, 4, 1, 6144, 4488, 3312, 1140, 240, 66, 4, 1, 15120, 31200, 14640, 6480, 2040, 312, 84, 4, 1, 122880, 104880, 97440, 37440, 11280, 3360, 392, 104, 4, 1, 332640

Offset

0,2

Comments

The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 2n/f(n-1,x), where f(0,n) = 1. (Sum of numbers in row n) = A249074(n) for n >= 0. (n-th term of column 1) = A087299(n) for n >= 1.

Links

Clark Kimberling, Rows 0..100, flattened

Example

f(0,x) = 1/1, so that p(0,x) = 1
f(1,x) = (4 + x)/1, so that p(1,x) = 4 + x;
f(2,x) = (6 + 4 x +  x^2)/(3 + x), so that p(2,x) = 6 + 4 x +  x^2).
First 6 rows of the triangle of coefficients:
1
4    1
6    4    1
32   14   4    1
60   72   24   4    1
384  228  120  36   4   1

Mathematica

z = 11; p[x_, n_] := x + 2 n/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}]] (* A249074 array *)
Flatten[CoefficientList[u, x]] (* A249074 sequence  *)
v = u /. x -> 1  (* A249075 *)
u /. x -> 0      (* A087299 *)

Crossrefs

Cf. A249057, A249075, A087299.

Sequence in context: A248416 A348853 A349238 * A021710 A127555 A192085

Adjacent sequences: A249071 A249072 A249073 * A249075 A249076 A249077

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Oct 20 2014

Status

approved