Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Jun 19 2023 05:26:17
%S 1,7,5,0,2,4,1,2,9,1,7,1,8,3,0,9,0,3,1,2,4,9,7,3,8,6,2,4,6,3,9,8,1,5,
%T 8,7,8,7,7,8,2,0,5,8,1,8,1,3,8,1,5,9,0,5,6,1,3,1,6,5,8,6,1,3,1,7,5,1,
%U 9,3,5,1,6,7,1,5,2,0,6,0,5,0,7,7,7,4,3,8,8,7,5,6,5,7,0,9,2,4,7,1,4,1,0,0,1
%N Decimal expansion of a constant related to Carlitz compositions (A003242).
%H Vaclav Kotesovec, <a href="/A241902/b241902.txt">Table of n, a(n) for n = 1..1500</a>
%H P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009, p. 201.
%H A. Knopfmacher and H. Prodinger, <a href="https://doi.org/10.1006/eujc.1998.0216">On Carlitz compositions</a>, European Journal of Combinatorics, Vol. 19, 1998, pp. 579-589.
%F Equals lim n -> infinity A003242(n)^(1/n).
%e 1.7502412917183090312497386246398158787782...
%t RealDigits[r /. FindRoot[Exp[QPolyGamma[0, 1 + Pi*I/Log[r], r]] == r^(3/2)/(1-r), {r, 3/2}, WorkingPrecision -> 120], 10, 110][[1]] (* _Vaclav Kotesovec_, Jun 19 2023 *)
%Y Cf. A003242, A224958, A212322, A106357, A261984, A106369.
%K nonn,cons
%O 1,2
%A _Vaclav Kotesovec_, May 01 2014