A226243 Denominators of the probability of success in sultan's dowry problem with n daughters.

1, 2, 2, 24, 30, 180, 70, 1120, 840, 8400, 630, 83160, 72072, 1009008, 1081080, 192192, 408408, 7351344, 2217072, 8868288, 203693490, 71131060, 74364290, 4759314560, 14872858000, 77338861600, 72282089880

Offset: 1

Author

José María Grau Ribas, Jun 01 2013

Keywords

• nonn
• frac

Examples

			1, 1/2, 1/2, 11/24, 13/30, 77/180, 29/70, 459/1120, ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Eric Weisstein's World of Mathematics, Sultan's Dowry Problem.
• Wikipedia, Secretary problem.

Crossrefs

Cf. A226242(numerators), A054404.

Programs

Mathematica

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}]

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