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A354556
Numerators of a sequence related to the Secretary Problem with Multiple Stoppings.
2
1, 3, 47, 2761, 4162637, 380537052235603, 705040594914523588948186792543, 302500210177484374840641189918370275991590974715547528765249, 49554292678269029432299170288905873298367846539726510384850403192729912522937262239403638817695466470734534217406992001
OFFSET
1,2
COMMENTS
exp(-A354556(n)/A354557(n)) is the asymptotic value of the n-th threshold in the Secretary Problem with n Stoppings.
LINKS
T. Matsui and K. Ano, Lower Bounds for Bruss' Odds Problem with Multiple Stoppings, arXiv:1204.5537 [math.NT], 2012-2017.
EXAMPLE
1, 3/2, 47/24, 2761/1152, 4162637/1474560, 380537052235603/117413668454400, 705040594914523588948186792543/193003573558876719588311040000
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[Numerator@S[n], {n, 1, 10}]
CROSSREFS
Cf. A354557 (denominators).
Sequence in context: A187665 A088718 A355256 * A219162 A016548 A208059
KEYWORD
nonn,frac
AUTHOR
STATUS
approved