|
%I #35 Jun 27 2021 03:35:49
%S 1,0,9,8,6,8,5,8,0,5,5,2,5,1,8,7,0,1,3,0,1,7,7,4,6,3,2,5,7,2,1,3,3,1,
%T 8,0,7,9,3,1,2,2,2,0,7,1,0,6,4,4,2,6,8,4,0,7,4,1,0,4,2,7,8,1,5,7,8,3,
%U 2,1,7,4,4,3,6,9,6,6,5,6,0,8,2,3,2,2,4,2,3,9,1,7,4,4,7,4,9,7,9,9,0,6,6,0,5
%N Decimal expansion of Lengyel's constant L.
%C L - log(Pi-1)/log(2) ~ 0.00000171037285384 ~ 1/Pi^11.5999410273. - _Gerald McGarvey_, Aug 17 2004
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 319 and 556.
%H László Babai and Tamás Lengyel, <a href="https://doi.org/10.1524/anly.1992.12.12.109">A convergence criterion for recurrent sequences with application to the partition lattice</a>, Analysis, Vol. 12, No. 1-2 (1992), pp. 109-120; <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.30.4586&rep=rep1&type=pdf">preprint</a>.
%H Tamás Lengyel, <a href="https://doi.org/10.1016/S0195-6698(84)80035-9">On a recurrence involving Stirling numbers</a>, European Journal of Combinatorics, Vol. 5, No. 4 (1984), pp. 313-321.
%H Tamás Lengyel, <a href="https://doi.org/10.1134/s2070046612030028">On some 2-adic properties of a recurrence involving Stirling numbers</a>, p-Adic Numbers Ultrametric Anal. Appl., Vol. 4, No. 3 (2012), pp. 179-186.
%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap54.html">The Lengyel constant</a>. [broken link]
%H Thomas Prellberg, <a href="http://algo.inria.fr/seminars/sem02-03/prellberg1-slides.ps">On the asymptotic analysis of a class of linear recurrences</a> (slides).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LengyelsConstant.html">Lengyel's Constant</a>.
%F Equals lim_{n->oo} A005121(n) * (2*log(2))^n * n^(1+log(2)/3) / n!^2. - _Amiram Eldar_, Jun 27 2021
%e 1.0986858055251870130177463257213318079312220710644268407410427815783217...
%Y Cf. A005121, A131407, A260932.
%K nonn,cons
%O 1,3
%A _Eric W. Weisstein_, Jul 07 2003
%E More terms from _Vaclav Kotesovec_, Mar 11 2014
|
