This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A226243 #19 Feb 16 2025 08:33:19
%S A226243 1,2,2,24,30,180,70,1120,840,8400,630,83160,72072,1009008,1081080,
%T A226243 192192,408408,7351344,2217072,8868288,203693490,71131060,74364290,
%U A226243 4759314560,14872858000,77338861600,72282089880
%N A226243 Denominators of the probability of success in sultan's dowry problem with n daughters.
%H A226243 Andrew Howroyd, <a href="/A226243/b226243.txt">Table of n, a(n) for n = 1..500</a>
%H A226243 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SultansDowryProblem.html">Sultan's Dowry Problem.</a>
%H A226243 Wikipedia, <a href="http://en.wikipedia.org/wiki/Secretary_problem">Secretary problem</a>.
%e A226243 1, 1/2, 1/2, 11/24, 13/30, 77/180, 29/70, 459/1120, ...
%t A226243 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 A226243 (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 A226243 Cf. A226242(numerators), A054404.
%K A226243 nonn,frac
%O A226243 1,2
%A A226243 _José María Grau Ribas_, Jun 01 2013