A339393 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.

1, 1, 4, 7, 28, 56, 88, 594, 5808, 415272, 8758464, 274431872, 12856077696, 905435186304, 481691519113728, 77763074616922464, 3824113551749834112, 1437016892446437662976, 165559472503434318118656, 146602912901791088694069888, 200050146291129782743679367168

Offset: 1

Author

Amiram Eldar, Dec 04 2020

Keywords

• nonn
• frac

Comments

See A339392 for details.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000045, A001791, A084623, A234951, A243398, A339392 (numerators).

Programs

Mathematica

f = Table[k/(Fibonacci[k + 2] - 1), {k, 2, 20}]; Denominator[1 - FoldList[Times, 1, f]]

Formula

a(n) = denominator(1 - Product_{k=2..n} k/(Fibonacci(k+2)-1)).