A354557 Denominators of a sequence related to the Secretary Problem with Multiple Stoppings.
1, 2, 24, 1152, 1474560, 117413668454400, 193003573558876719588311040000, 74500758812993473612938854416966977838930799571763200000000, 11100726127423649454784549321327362347631758176882955145554591521918123315624957195621435513013513748480000000000000000
Offset: 1
Links
- T. Matsui and K. Ano, Lower Bounds for Bruss' Odds Problem with Multiple Stoppings, arXiv:1204.5537 [math.NT], 2012-2017.
Crossrefs
Cf. A354556 (numerators).
Programs
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Mathematica
la[1]=1;alfa[k_,1]=1/k!;alfa[k_,k_]:=1;la[k_]:=la[k]=1-alfa[k,k-1]; 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}]; S[n_]:=Sum[la[i],{i,1,n}]; Table[Denominator@S[n],{n,1,10}]