OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Jesús Guillera and Jonathan Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, arXiv:math/0506319 [math.NT], 2005-2006; Ramanujan J., Vol. 16 (2008), pp. 247-270; see Example 5.5.
Yong Kong, Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density, arXiv:cond-mat/0610690, 2006.
Eric Weisstein's World of Mathematics, Domino Tiling
FORMULA
Equals Catalan/Pi.
Also equals integral_{t=-Pi..Pi} arccosh(sqrt(cos(t)+3)/sqrt(2))/(4*Pi) dt. - Jean-François Alcover, May 14 2014
From Antonio Graciá Llorente, Oct 11 2024: (Start)
Equals Sum_{n>=0} (n/2^(n + 2)) * Sum_{k>=0} (-1)^(k + 1)*binomial(n, k)*log(2*k + 1), (Guillera and Sondow, 2008).
Equals Sum_{n>=1} n*(arccoth((4*n)/3) - 3*arccoth(4*n)). (End)
EXAMPLE
0.29156090403081878013...
MATHEMATICA
RealDigits[Catalan/Pi, 10, 100][[1]] (* G. C. Greubel, Aug 24 2018 *)
PROG
(PARI) default(realprecision, 100); Catalan/Pi \\ G. C. Greubel, Aug 24 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Catalan(R)/Pi(R); // G. C. Greubel, Aug 24 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jul 31 2008
STATUS
approved