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%I #18 Nov 14 2018 13:33:48
%S 1,2,2,24,30,180,70,1120,840,8400,630,83160,72072,1009008,1081080,
%T 192192,408408,7351344,2217072,8868288,203693490,71131060,74364290,
%U 4759314560,14872858000,77338861600,72282089880
%N Denominators of the probability of success in sultan's dowry problem with n daughters.
%H Andrew Howroyd, <a href="/A226243/b226243.txt">Table of n, a(n) for n = 1..500</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SultansDowryProblem.html">Sultan's Dowry Problem.</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Secretary_problem">Secretary problem</a>.
%e 1, 1/2, 1/2, 11/24, 13/30, 77/180, 29/70, 459/1120, ...
%t G[k_, n_] := G[k, n] = 1/( k + 1) Max[(k + 1)/n, G[k + 1, n]] + k/(k + 1)G[k + 1, n]; G[n_, n_] = 0; Denominator@Table[G[0, n], {n, 1, 20}]
%o (PARI) a(n)={my(g=0); forstep(k=n-1, 0, -1, g = max(1/n, g/(k+1)) + k*g/(k+1)); denominator(g)} \\ _Andrew Howroyd_, Nov 12 2018
%Y Cf. A226242(numerators), A054404.
%K nonn,frac
%O 1,2
%A _José María Grau Ribas_, Jun 01 2013