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

2,1

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.

Links

Table of n, a(n) for n=2..10.

Mathematica

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

Prog

(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

Crossrefs

Cf. A094638.

Sequence in context: A246861 A305601 A202027 * A018036 A007050 A320811

Adjacent sequences: A374955 A374956 A374957 * A374959 A374960 A374961

Keyword

nonn,more

Author

Matthew McMullen, Aug 05 2024

Extensions

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

Status

approved