%I #19 Nov 14 2018 13:33:40
%S 1,1,1,11,13,77,29,459,341,3349,251,32891,28271,395243,420983,74587,
%T 158183,2833255,853661,3407275,77976391,27223837,28399557,1814074083,
%U 5665315119,29397421371,27452509171,85332099113,88200436013
%N Numerators of the probability of success in sultan's dowry problem with n daughters.
%H Andrew Howroyd, <a href="/A226242/b226242.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; Numerator@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)); numerator(g)} \\ _Andrew Howroyd_, Nov 12 2018
%Y Cf. A226243 (denominators), A054404.
%K nonn,frac
%O 1,4
%A _José María Grau Ribas_, Jun 01 2013