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%I #34 Nov 14 2018 01:05:51
%S 1,3,15,105,2835,31185,2027025,91216125,10854718875,206239658625,
%T 7795859096025,4482618980214375,72512954091703125,
%U 99850337784275203125,37643577344671751578125,8168656283793770092453125,12518528979807790079765625
%N 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.
%C Denominators of the probability function defined in A231580.
%F 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
%e 1, 2/3, 7/15, 34/105, 638/2835, 4876/31185, 220217/2027025, 6885458/91216125, 569311642/10854718875, 7515775348/206239658625, 197394815194/7795859096025, ...
%t 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);
%t f[{_}] = f[{_}, _] = 1;
%t f[ConstantArray[0, #], 2] & /@ Range[2, 20] // Denominator
%o (PARI) f=[1]; for(n=2, 25, f=concat(f, sum(k=1, n-1, (f[k]*f[n-k])) / (2*n-3))); f
%o vector(#f, k, denominator(f[k])) \\ _Colin Barker_, Jul 24 2014, sequence shifted by 1 index
%Y Cf. A231580.
%K nonn,frac
%O 1,2
%A _Philipp O. Tsvetkov_, Nov 12 2013
%E More terms from _Colin Barker_, Jul 24 2014
%E Name edited by _Jon E. Schoenfield_, Nov 13 2018
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