This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A354556 #22 Aug 01 2022 08:11:18
%S A354556 1,3,47,2761,4162637,380537052235603,705040594914523588948186792543,
%T A354556 302500210177484374840641189918370275991590974715547528765249,
%U A354556 49554292678269029432299170288905873298367846539726510384850403192729912522937262239403638817695466470734534217406992001
%N A354556 Numerators of a sequence related to the Secretary Problem with Multiple Stoppings.
%C A354556 exp(-A354556(n)/A354557(n)) is the asymptotic value of the n-th threshold in the Secretary Problem with n Stoppings.
%H A354556 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.
%e A354556 1, 3/2, 47/24, 2761/1152, 4162637/1474560, 380537052235603/117413668454400, 705040594914523588948186792543/193003573558876719588311040000
%t A354556 la[1]=1;alfa[k_,1]=1/k!;alfa[k_,k_]:=1;la[k_]:=la[k]=1-alfa[k,k-1];
%t A354556 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 A354556 S[n_]:=Sum[la[i],{i,1,n}];
%t A354556 Table[Numerator@S[n],{n,1,10}]
%Y A354556 Cf. A354557 (denominators).
%K A354556 nonn,frac
%O A354556 1,2
%A A354556 _José María Grau Ribas_, May 28 2022