A241902 - 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