A274169 - OEIS

A274169

Decimal expansion of 1/exp(exp(1)-1).

1, 7, 9, 3, 7, 4, 0, 7, 8, 7, 3, 4, 0, 1, 7, 1, 8, 1, 9, 6, 1, 9, 8, 9, 5, 8, 7, 3, 1, 8, 3, 1, 6, 4, 9, 8, 4, 5, 9, 6, 8, 1, 6, 0, 1, 7, 5, 8, 9, 1, 5, 6, 1, 3, 1, 5, 7, 3, 7, 0, 4, 2, 1, 6, 0, 2, 4, 8, 3, 7, 6, 0, 8, 1, 1, 6, 4, 5, 7, 2, 8, 8, 0, 1, 3, 0, 9, 4, 1, 4, 1, 1, 2, 4, 3, 8, 0, 0, 4, 6, 0, 5, 6, 0

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OFFSET

0,2

COMMENTS

This is the limiting value of the probability that a random n-permutation will have no cycles of length less than k (for any k) as n goes to infinity. For example, the probability (as n goes to infinity) that a random n-permutation has no fixed points is 1/exp(1). The probability that it has no cycles of length 1 or 2 is 1/exp(1+1/2). The probability that it has no cycles of length 1 or 2 or 3 is 1/exp(1+1/2+1/3!)...

LINKS

Table of n, a(n) for n=0..103.

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 228.

FORMULA

Equals 1/A234473. - Michel Marcus, Jun 12 2016

EXAMPLE

0.1793740787340171819619895873183164984596816...

MAPLE

Digits:=100: evalf(1/exp(exp(1)-1)); # Wesley Ivan Hurt, Jun 11 2016

MATHEMATICA

RealDigits[1/E^(E - 1), 10, 50][[1]]

PROG