(OEIS A072508). This limit was subsequently shown to exist by P. Flajolet. Note that , which follows from the radius
of convergence of the reciprocal power series.

The continued fraction of Backhouse's constant is [1, 2, 5, 5, 4, 1, 1, 18, 1, 1, 1, 1, 1, 2, ...] (OEIS A074269),
which is also the same as the continued fraction of except for a leading 0 in the latter.

Finch, S. R. "Kalmár's Composition Constant." §5.5 in Mathematical
Constants. Cambridge, England: Cambridge University Press, pp. 292-295,
2003.Finch, S. "Kalmár's Composition Constant." http://algo.inria.fr/bsolve/.Sloane,
N. J. A. Sequences A030018, A072508,
A074269, and A088751
in "The On-Line Encyclopedia of Integer Sequences."