A249248 - OEIS

%I #16 Oct 30 2014 18:32:20

%S 1,1,3,1,7,3,1,12,22,3,1,18,69,40,3,1,25,159,241,61,3,1,33,310,883,

%T 582,85,3,1,42,543,2465,3393,1155,112,3,1,52,882,5798,13805,9786,2032,

%U 142,3,1,63,1354,12110,44253,57521,23368,3294,175,3,1,75,1989

%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 + 1 + n*x/f(n-1,x), where f(1,x) = 1.

%H Clark Kimberling, <a href="/A249248/b249248.txt">Table of n, a(n) for n = 1..5050</a>

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

%e f(2,x) = (1 + 3 x)/1, so that p(2,x) = 1 + 3 x;

%e f(3,x) = (1 + 7 x + 3 x^2)/(1 + 3 x), so that p(3,x) = 1 + 7 x + 3 x^2.

%e First 6 rows of the triangle of coefficients:

%e 1

%e 1      3

%e 1      7      3

%e 1      12     22     3

%e 1      18     69     40    3

%e 1      25     150    241   61    3

%t z = 14; f[n_, x_] := x + 1 + n*x/f[n - 1, x]; f[1, x_] = 1;

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

%t u = Numerator[t]

%t TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (*A249248 array*)

%t Flatten[CoefficientList[u, x]] (*A249248 sequence*)

%o (PARI) rown(n) = if (n==1, 1, x + 1 + n*x/rown(n-1));

%o tabl(nn) = for (n=1, nn, print(Vecrev(numerator(rown(n))))); \\ _Michel Marcus_, Oct 30 2014

%Y Cf. A249247.

%K nonn,tabl,easy

%O 1,3

%A _Clark Kimberling_, Oct 24 2014