cp's OEIS Frontend

A231732 Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 2)/(x + 1).

%I A231732 #5 Nov 02 2014 12:18:36
%S A231732 2,1,5,6,2,12,22,14,3,29,72,69,30,5,70,219,280,182,60,8,169,638,1021,
%T A231732 884,436,116,13,408,1804,3468,3750,2460,978,218,21,985,4992,11206,
%U A231732 14532,11895,6288,2095,402,34,2378,13589,34888,52760,51750,34119,15112,4334
%N A231732 Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the numerator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 2)/(x + 1).
%C A231732 Sum of numbers in row n:  A015521(n).  Left edge:  A000129.  Right edge:  A000045 (Fibonacci numbers).
%e A231732 First 3 rows:
%e A231732 2 .... 1
%e A231732 5 .... 6 .... 2
%e A231732 12 ... 22 ... 14 ... 3
%e A231732 First 3 polynomials:  2 + x, 5 + 6*x + 2*x^2, 12 + 22*x + 14*x^2 + 3*x^3.
%t A231732 t[n_] := t[n] = Table[(x + 2)/(x + 1), {k, 0, n}];
%t A231732 b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];
%t A231732 p[x_, n_] := p[x, n] = Last[Expand[Numerator[b]]][[n]];
%t A231732 u = Table[p[x, n], {n, 1, 10}]
%t A231732 v = CoefficientList[u, x]; Flatten[v]
%Y A231732 Cf. A230000, A231733.
%K A231732 nonn,tabf
%O A231732 1,1
%A A231732 _Clark Kimberling_, Nov 13 2013