A249130 - OEIS

%I #17 Feb 28 2025 07:45:23

%S 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,

%T 384,400,368,232,56,30,2,1,384,1536,1232,688,408,72,38,2,1,3840,4384,

%U 5216,3552,1248,708,92,48,2,1,3840,19200,16704,12096,7632,1968,1088,112,58,2,1

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

%C 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.

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

%C (Column 1) = A037223.

%H Clark Kimberling, <a href="/A249130/b249130.txt">Rows 0..100, flattened</a>

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

%e f(1,x) = (2 + x)/1, so that p(1,x) = 2 + x;

%e f(2,x) = (2 + 2*x + x^2)/(3 + x), so that p(2,x) = 2 + 2*x + x^2.

%e First 6 rows of the triangle of coefficients:

%e   1

%e   2    1

%e   2    2    1

%e   8    6    2    1

%e   8    16   10   2    1

%e   48   44   28   16   2   1

%t z = 15; p[x_, n_] := x + 2 Floor[n/2]/p[x, n - 1]; p[x_, 1] = 1;

%t t = Table[Factor[p[x, n]], {n, 1, z}]

%t u = Numerator[t]

%t TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249130 array *)

%t Flatten[CoefficientList[u, x]] (* A249130 sequence *)

%Y Cf. A249131, A037223, A249128.

%K nonn,tabl,easy,changed

%O 0,2

%A _Clark Kimberling_, Oct 22 2014