A354557 - OEIS

%I #17 Aug 01 2022 08:11:11

%S 1,2,24,1152,1474560,117413668454400,193003573558876719588311040000,

%T 74500758812993473612938854416966977838930799571763200000000,

%U 11100726127423649454784549321327362347631758176882955145554591521918123315624957195621435513013513748480000000000000000

%N Denominators of a sequence related to the Secretary Problem with Multiple Stoppings.

%H T. Matsui and K. Ano, <a href="https://arxiv.org/abs/1204.5537">Lower Bounds for Bruss' Odds Problem with Multiple Stoppings</a>, arXiv:1204.5537 [math.NT], 2012-2017.

%t la[1]=1;alfa[k_,1]=1/k!;alfa[k_,k_]:=1;la[k_]:=la[k]=1-alfa[k,k-1];

%t alfa[k_,kp_]:=alfa[k,kp]= la[kp]^(1+k-kp)/(1+k-kp)!+Sum[la[kp]^b/b! alfa[k-b,kp-1],{b,0,k-kp}];

%t S[n_]:=Sum[la[i],{i,1,n}];

%t Table[Denominator@S[n],{n,1,10}]

%Y Cf. A354556 (numerators).

%K nonn,frac

%O 1,2

%A _José María Grau Ribas_, May 28 2022