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%I #9 Oct 16 2023 01:46:36
%S 1,1,4,7,28,56,88,594,5808,415272,8758464,274431872,12856077696,
%T 905435186304,481691519113728,77763074616922464,3824113551749834112,
%U 1437016892446437662976,165559472503434318118656,146602912901791088694069888,200050146291129782743679367168
%N Denominators of the probability that when a stick is broken up at n-1 points independently and uniformly chosen at random along its length there exist 3 of the n pieces that can form a triangle.
%C See A339392 for details.
%H Amiram Eldar, <a href="/A339393/b339393.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = denominator(1 - Product_{k=2..n} k/(Fibonacci(k+2)-1)).
%t f = Table[k/(Fibonacci[k + 2] - 1), {k, 2, 20}]; Denominator[1 - FoldList[Times, 1, f]]
%Y Cf. A000045, A001791, A084623, A234951, A243398, A339392 (numerators).
%K nonn,frac
%O 1,3
%A _Amiram Eldar_, Dec 04 2020
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