A231634 a(n) is the denominator of the probability that n segments of length 2, each placed randomly on a line segment of length 2n, will completely cover the line segment.
1, 3, 15, 105, 2835, 31185, 2027025, 91216125, 10854718875, 206239658625, 7795859096025, 4482618980214375, 72512954091703125, 99850337784275203125, 37643577344671751578125, 8168656283793770092453125, 12518528979807790079765625
Offset: 1
Examples
1, 2/3, 7/15, 34/105, 638/2835, 4876/31185, 220217/2027025, 6885458/91216125, 569311642/10854718875, 7515775348/206239658625, 197394815194/7795859096025, ...
Crossrefs
Cf. A231580.
Programs
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Mathematica
f[g_List, l_] := f[g, l] = Sum[f[g[[;; n]], l] f[g[[n + 1 ;;]], l], {n, Length[g] - 1}]/(Total[l + g] - 2 l + 1); f[{}] = f[{}, _] = 1; f[ConstantArray[0, #], 2] & /@ Range[2, 20] // Denominator -
PARI
f=[1]; for(n=2, 25, f=concat(f, sum(k=1, n-1, (f[k]*f[n-k])) / (2*n-3))); f vector(#f, k, denominator(f[k])) \\ Colin Barker, Jul 24 2014, sequence shifted by 1 index
Formula
Denominator of f(n) where f(0)=1 and f(n) = Sum_{k=0..n-1} f(n)*f(n-k-1)/(2*n-1). - Michael Somos, Mar 01 2014
Extensions
More terms from Colin Barker, Jul 24 2014
Name edited by Jon E. Schoenfield, Nov 13 2018
Comments