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

Offset: 0

Author

Geoffrey Critzer, Jun 11 2016

Keywords

• nonn
• cons

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!)...

Examples

			0.1793740787340171819619895873183164984596816...
		

Links

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

Crossrefs

Cf. A000166, A038205, A047865, A234473.

Programs

Maple

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

Mathematica

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

PARI

1/exp(exp(1)-1) \\ Michel Marcus, Jun 12 2016

Formula

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