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.

2, 7, 21, 57, 157, 430, 1173, 3199, 8717

Offset: 2

Author

Matthew McMullen, Aug 05 2024

Keywords

• nonn
• more

Comments

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.

The ratio of successive terms seems to be converging to e.

References

• M. Ahsanullah and V. B. Nevzorov, Records via Probability Theory, Atlantis Press, 2015.

Crossrefs

Cf. A094638.

Programs

Mathematica

Solve[Sum[Abs[StirlingS1[k-1,n-1]]/k!,{k,n,x}]>=.5 && x>=n, x, Integers]

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

Extensions

a(9)-a(10) from Sean A. Irvine, Aug 26 2024