cp's OEIS Frontend

A231730 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 + 1/2.

%I A231730 #9 Nov 02 2014 12:18:36
%S A231730 1,2,5,4,4,9,22,12,8,29,56,72,32,16,65,202,232,208,80,32,181,556,924,
%T A231730 800,560,192,64,441,1726,2964,3480,2480,1440,448,128,1165,4832,10112,
%U A231730 12608,11680,7168,3584,1024,256,2929,14066,31632,46752,46816,36288,19712
%N A231730 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 + 1/2.
%C A231730 Sum of numbers in row n:  A015521(n).  Left edge:  A006131.  Right edge:  powers of 2
%e A231730 First 3 rows:
%e A231730 1 .... 2
%e A231730 5 .... 4 .... 4
%e A231730 9 .... 22 ... 12 ... 8
%e A231730 First 3 polynomials:  1 + 2*x, 5 + 4*x + 4*x^2, 9 + 22*x + 12*x^2 + 8*x^3.
%t A231730 t[n_] := t[n] = Table[x + 1/2, {k, 0, n}];
%t A231730 b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];
%t A231730 p[x_, n_] := p[x, n] = Last[Expand[Numerator[b]]][[n]];
%t A231730 u = Table[p[x, n], {n, 1, 10}]
%t A231730 v = CoefficientList[u, x]; Flatten[v]
%Y A231730 Cf. A230000, A231731.
%K A231730 nonn,tabf
%O A231730 1,2
%A A231730 _Clark Kimberling_, Nov 13 2013