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

1,2

Comments

Denominators of the probability function defined in A231580.

Links

Table of n, a(n) for n=1..17.

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

Example

1, 2/3, 7/15, 34/105, 638/2835, 4876/31185, 220217/2027025, 6885458/91216125, 569311642/10854718875, 7515775348/206239658625, 197394815194/7795859096025, ...

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

Prog

(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

Crossrefs

Cf. A231580.

Sequence in context: A129731 A269455 A088109 * A353587 A128276 A295124

Adjacent sequences: A231631 A231632 A231633 * A231635 A231636 A231637

Keyword

nonn,frac

Author

Philipp O. Tsvetkov, Nov 12 2013

Extensions

More terms from Colin Barker, Jul 24 2014

Name edited by Jon E. Schoenfield, Nov 13 2018

Status

approved