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 A374958 #32 Sep 03 2024 01:29:33
%S A374958 2,7,21,57,157,430,1173,3199,8717
%N A374958 Median, as a function of n, of the probability mass function s(k-1,n-1)/k!, where k>=n and s(a,b) denotes the unsigned Stirling number of the first kind.
%C A374958 This probability mass function occurs in the statistics of records, specifically, it is the probability that the n-th record is set on the k-th race.
%C A374958 The ratio of successive terms seems to be converging to e.
%D A374958 M. Ahsanullah and V. B. Nevzorov, Records via Probability Theory, Atlantis Press, 2015.
%t A374958 Solve[Sum[Abs[StirlingS1[k-1,n-1]]/k!,{k,n,x}]>=.5 && x>=n, x, Integers]
%o A374958 (PARI) a(n)=my(s=0); for(x=n, oo, s+=abs(stirling(x-1,n-1,1))/x!; if(2*s >= 1, return(x))) \\ _Andrew Howroyd_, Aug 09 2024
%Y A374958 Cf. A094638.
%K A374958 nonn,more
%O A374958 2,1
%A A374958 _Matthew McMullen_, Aug 05 2024
%E A374958 a(9)-a(10) from _Sean A. Irvine_, Aug 26 2024