%I A097675
%S A097675 3,3,3,3,2,5,2,1,2,6,5,8,5,4,1,7,2,1,5,4,0,0,3,9,0,7,6,9,7,2,1,0,2,2,1,
%T A097675 1,7,4,3,9,8,0,2,5,9,7,2,7,6,5,5,4,6,9,6,6,2,8,2,7,2,9,1,3,5,2,7,9,3,4,
%U A097675 3,6,8,2,1,4,6,6,0,7,0,5,8,9,7,4,3,8,2,5,4,1,8,2,9,5,0,2,6,6,2,0,6,3,4
%N A097675 Decimal expansion of the constant 8*exp(psi(5/8)+EulerGamma), where EulerGamma 
               is the Euler-Mascheroni constant (A001620).
%C A097675 This constant appears in Benoit Cloitre's generalized Euler-Gauss formula 
               for the Gamma function (see Cloitre link) and is involved in the 
               exact determination of asymptotic limits of certain order-8 linear 
               recursions with varying coefficients (see A097682 for example).
%D A097675 A. M. Odlyzko, Linear recurrences with varying coefficients, in Handbook 
               of Combinatorics, Vol. 2, R. L. Graham, M. Grotschel and L. Lovasz, 
               eds., Elsevier, Amsterdam, 1995, pp. 1135-1138.
%H A097675 Benoit Cloitre, <a href="http://www.lacim.uqam.ca/~plouffe/OEIS/archive_in_pdf/
               CloitreGammaConstants.pdf">On a generalization of Euler-Gauss formula 
               for the Gamma function</a>, pre-print 2004.
%H A097675 Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/
               Constants/Miscellaneous/gammaFunction.html">Introduction to the Gamma 
               Function</a>.
%H A097675 Andrew Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/doc/asymptotic.enum.pdf">
               Asymptotic enumeration methods</a>, in Handbook of Combinatorics, 
               vol. 2, 1995, pp. 1063-1229.
%F A097675 c = (1+sqrt(2))^(sqrt(2))/2*exp(Pi/2*(sqrt(2)-1))
%e A097675 c = 3.33325212658541721540039076972102211743980259727655469662827...
%t A097675 RealDigits[(1 + Sqrt[2])^(Sqrt[2])/2E^(Pi/2*(Sqrt[2] - 1)), 10, 105][[1]] 
               (from Robert G. Wilson v Aug 27 2004)
%o A097675 (PARI) 8*exp(psi(5/8)+Euler)
%Y A097675 Cf. A097663-A097674, A097676.
%Y A097675 Sequence in context: A081334 A106694 A031355 this_sequence A141605 A073139 
               A122845
%Y A097675 Adjacent sequences: A097672 A097673 A097674 this_sequence A097676 A097677 
               A097678
%K A097675 cons,nonn
%O A097675 1,1
%A A097675 Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2004
%E A097675 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 27 2004