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A138704 Irregular array read by rows: row n contains the continued fraction terms (in order) for the absolute value of B_{2n}, the (2n)th Bernoulli number.

%I A138704 #14 Oct 18 2017 22:50:27
%S A138704 1,0,6,0,30,0,42,0,30,0,13,5,0,3,1,19,3,11,1,6,7,10,1,5,1,2,2,54,1,33,
%T A138704 1,2,3,2,529,8,20,2,6192,8,8,2,86580,3,1,19,3,11,1425517,6,27298231,
%U A138704 14,1,2,1,14,601580873,1,9,15,2,7,6,15116315767,10,1,5,1,2,2,429614643061,6
%N A138704 Irregular array read by rows: row n contains the continued fraction terms (in order) for the absolute value of B_{2n}, the (2n)th Bernoulli number.
%C A138704 The number of terms in row n is A138705(n).
%H A138704 Michael De Vlieger, <a href="/A138704/b138704.txt">Table of n, a(n) for n = 0..2884</a>
%e A138704 The 12th Bernoulli number is -691/2730. Now 691/2730 has the continued fraction 0 + 1/(3 + 1/(1 + 1/(19 + 1/(3 + 1/11)))). So row 6 is (0,3,1,19,3,11).
%p A138704 A138704row := proc(n) local B; B := abs(bernoulli(2*n)) ; numtheory[cfrac](B,20,'quotients') ; end: seq(op(A138704row(n)),n=0..20) ; # _R. J. Mathar_, Jul 20 2009
%t A138704 Array[ContinuedFraction@ Abs@ BernoulliB[2 #] &, 18, 0] // Flatten (* _Michael De Vlieger_, Oct 18 2017 *)
%Y A138704 Cf. A138701, A138705, A138706, A000367, A002445.
%K A138704 nonn,tabf
%O A138704 0,3
%A A138704 _Leroy Quet_, Mar 26 2008
%E A138704 More terms from _R. J. Mathar_, Jul 20 2009