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%I #10 Jun 28 2019 08:59:11
%S 1,3,6,5,45,63,420,405,14175,17325,187110,552825,14189175,49116375,
%T 729729000,723647925,8881133625,109185701625,2062396586250,
%U 10257709336875,428772250281375,2348038513445625,53791427762572500,160789593855515625,16025362854266390625
%N Denominator of the expected fraction of occupied places on n-length lattice randomly filled with 2-length segments.
%C The limit of expected fraction of occupied places on n-length lattice randomly filled with 2-length segments at n tends to infinity is equal to 1-1/e^2 (see A219863).
%H D. G. Radcliffe, <a href="https://mathblag.files.wordpress.com/2012/12/fatmen.pdf">Fat men sitting at a bar</a>
%F Denominator of f(n), where f(0)=0; f(1)=0 and f(n) = (2 + 2(n-2)f(n-2) + (n-1)(n-2)f(n-1))/(n(n-1)) for n>1.
%e 0, 1, 2/3, 5/6, 4/5, 37/45, 52/63, 349/420, 338/405, 11873/14175, ...
%t RecurrenceTable[{f[n] == (2 + 2 (n - 2) f[n - 2] + (n - 1) (n - 2) f[n - 1])/(n (n - 1)), f[0] == 0, f[1] == 0}, f, {n, 2, 100}] // Denominator
%Y Cf. A219863, A231580, A307131 (numerators).
%K nonn,frac
%O 1,2
%A _Philipp O. Tsvetkov_, Mar 26 2019