A249139 - OEIS

%I #6 Oct 28 2014 00:10:41

%S 1,3,1,5,2,11,7,1,21,16,3,43,41,12,1,85,94,34,4,171,219,99,18,1,341,

%T 492,261,60,5,683,1101,678,195,25,1,1365,2426,1692,576,95,6,2731,5311,

%U 4149,1644,340,33,1,5461,11528,9959,4488,1106,140,7,10923,24881

%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) = 1 + (x + 2)/f(n-1,x), where f(0,x) = 1.

%C (Sum of numbers in row n) = A006130(n+1) for n >= 0.

%C (Column 1) is essentially A001045.

%H Clark Kimberling, <a href="/A249139/b249139.txt">Rows 0..100, flattened</a>

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

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

%e f(2,x) = (5 + 2 x)/(3 + x), so that p(2,x) = 5 + 2 x.

%e First 6 rows of the triangle of coefficients:

%e 1

%e 3    1

%e 5    2

%e 11   7    1

%e 21   16   3

%e 43   41   12  1

%t z = 15; f[x_, n_] := 1 + (x + 2)/f[x, n - 1]; f[x_, 1] = 1;

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

%t u = Numerator[t]

%t TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249139 array *)

%t Flatten[CoefficientList[u, x]] (* A249139 sequence *)

%Y Cf. A006130, A001045.

%K nonn,tabf,easy

%O 0,2

%A _Clark Kimberling_, Oct 23 2014