cp's OEIS Frontend

A231775 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 denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x + 2).

%I A231775 #5 Nov 02 2014 12:18:36
%S A231775 2,1,2,3,1,10,17,10,2,18,47,45,19,3,58,173,210,129,40,5,130,491,769,
%T A231775 642,302,76,8,362,1545,2850,2940,1830,687,144,13,882,4391,9565,11925,
%U A231775 9315,4671,1469,265,21,2330,12901,31898,46195,43170,26994,11294,3049,482
%N A231775 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 denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x + 2).
%C A231775 Sum of numbers in row n:  3*A002534(n).  Left edge:  2*A006131.  Right edge:  A000045 (Fibonacci numbers).
%e A231775 First 3 rows:
%e A231775 2 .... 1
%e A231775 2 .... 3 .... 1
%e A231775 10 ... 17 ... 10 ... 2
%e A231775 First 3 polynomials:  2 + x, 2 + 3*x + x^2, 10 + 17*x + 10*x^2 + 2*x^3.
%t A231775 t[n_] := t[n] = Table[(x + 1)/(x + 2), {k, 0, n}];
%t A231775 b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];
%t A231775 p[x_, n_] := p[x, n] = Last[Expand[Denominator[b]]][[n]];
%t A231775 u = Table[p[x, n], {n, 1, 10}]
%t A231775 v = CoefficientList[u, x]; Flatten[v]
%Y A231775 Cf. A230000, A231774, A000045.
%K A231775 nonn,tabf
%O A231775 1,1
%A A231775 _Clark Kimberling_, Nov 13 2013