A226242 Numerators of the probability of success in sultan's dowry problem with n daughters.

1, 1, 1, 11, 13, 77, 29, 459, 341, 3349, 251, 32891, 28271, 395243, 420983, 74587, 158183, 2833255, 853661, 3407275, 77976391, 27223837, 28399557, 1814074083, 5665315119, 29397421371, 27452509171, 85332099113, 88200436013

Offset

1,4

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.

Example

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

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; Numerator@Table[G[0, n], {n, 1, 20}]

Prog

(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

Crossrefs

Cf. A226243 (denominators), A054404.

Sequence in context: A057189 A072580 A186640 * A116436 A185240 A056446

Adjacent sequences: A226239 A226240 A226241 * A226243 A226244 A226245

Keyword

nonn,frac

Author

José María Grau Ribas, Jun 01 2013

Status

approved