A354557 Denominators of a sequence related to the Secretary Problem with Multiple Stoppings.

1, 2, 24, 1152, 1474560, 117413668454400, 193003573558876719588311040000, 74500758812993473612938854416966977838930799571763200000000, 11100726127423649454784549321327362347631758176882955145554591521918123315624957195621435513013513748480000000000000000

Offset

1,2

Links

Table of n, a(n) for n=1..9.

T. Matsui and K. Ano, Lower Bounds for Bruss' Odds Problem with Multiple Stoppings, arXiv:1204.5537 [math.NT], 2012-2017.

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}]

Crossrefs

Cf. A354556 (numerators).

Sequence in context: A330087 A357827 A307157 * A137887 A232310 A350792

Adjacent sequences: A354554 A354555 A354556 * A354558 A354559 A354560

Keyword

nonn,frac

Author

José María Grau Ribas, May 28 2022

Status

approved