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 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
 1, 3, 15, 105, 2835, 31185, 2027025, 91216125, 10854718875, 206239658625, 7795859096025, 4482618980214375, 72512954091703125, 99850337784275203125, 37643577344671751578125, 8168656283793770092453125, 12518528979807790079765625 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 2 11:44 EDT 2023. Contains 363097 sequences. (Running on oeis4.)