Wolfdieter Lang, Jun 21 2011
 Rationals r(n):= A191998(n)/A191999(n), n=1..20:

 [1, 3/2, 9/8, 21/16, 231/160, 847/640, 2541/2048, 16093/12288, 33649/24576, 43263/32768, 447051/327680, 1043119/786432, 13560547/10485760, 83300503/62914560, 170222767/125829120, 222599003/167772160, 13133341177/9730785280, 774867129443/583847116800, 4719645242971/3503082700800, 335094812250941/245215789056000]

 Numerators(r(n))=A191998(n), n=1..20:
 [1, 3, 9, 21, 231, 847, 2541, 16093, 33649, 43263, 447051, 1043119, 13560547, 83300503, 170222767, 222599003, 13133341177, 774867129443, 4719645242971, 335094812250941];

 Denominators(r(n))=A191999(n), n=1..20:
 [1, 2, 8, 16, 160, 640, 2048, 12288, 24576, 32768, 327680, 786432, 10485760, 62914560, 125829120, 167772160, 9730785280, 583847116800, 3503082700800, 245215789056000]

 Limit: r = lim_{n->infty} r(n) approximately 2*.6864067 = 1.3728134 (as given in the K. Conrad reference, Exercise 2, p. 134)

 r(10^N) for N=1..4, is (maple13 10 digits): 1.320281982, 1.367330607, 1.370967981, 1.372427437.

 #####################e.o.f. ###############################