A249074 - OEIS

%I #7 Oct 28 2014 00:00:07

%S 1,4,1,6,4,1,32,14,4,1,60,72,24,4,1,384,228,120,36,4,1,840,1392,564,

%T 176,50,4,1,6144,4488,3312,1140,240,66,4,1,15120,31200,14640,6480,

%U 2040,312,84,4,1,122880,104880,97440,37440,11280,3360,392,104,4,1,332640

%N Triangular array read by rows:  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 + 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.

%H Clark Kimberling, <a href="/A249074/b249074.txt">Rows 0..100, flattened</a>

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

%e f(1,x) = (4 + x)/1, so that p(1,x) = 4 + x;

%e f(2,x) = (6 + 4 x +  x^2)/(3 + x), so that p(2,x) = 6 + 4 x +  x^2).

%e First 6 rows of the triangle of coefficients:

%e 1

%e 4    1

%e 6    4    1

%e 32   14   4    1

%e 60   72   24   4    1

%e 384  228  120  36   4   1

%t z = 11; p[x_, n_] := x + 2 n/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}]] (* A249074 array *)

%t Flatten[CoefficientList[u, x]] (* A249074 sequence  *)

%t v = u /. x -> 1  (* A249075 *)

%t u /. x -> 0      (* A087299 *)

%Y Cf. A249057, A249075, A087299.

%K nonn,tabl,easy

%O 0,2

%A _Clark Kimberling_, Oct 20 2014