  We consider a family of integer sequences generated by nonlinear recurrences
of the second order, which have the curious property that the terms of the
sequence, and integer multiples of the ratios of successive terms (which are
also integers), appear interlaced in the continued fraction expansion of the
sum of the reciprocals of the terms. Using the rapid (double exponential)
growth of the terms, for each sequence it is shown that the sum of the
reciprocals is a transcendental number.
