OFFSET
1,2
COMMENTS
Average length of the 2nd increasing run in a random permutation of n integers as n->Infinity.
REFERENCES
Donald E. Knuth, The Art of Computer Programming, Vol. 3: Sorting and Searching, 2nd ed., Reading, MA: Addison-Wesley, 1998, p. 40.
François Le Lionnais, Les Nombres Remarquables, Paris, Hermann, 1983, p. 42.
LINKS
Eric Weisstein's World of Mathematics, Permutation.
FORMULA
Equals (Sum_{n>0}(Sum_{k>0} 1/(n!*k!)))-1. - Fredrik Johansson, Apr 21 2006
EXAMPLE
-2*e + e^2 = 1.95249244...
MATHEMATICA
RealDigits[E^2-2*E, 10, 120][[1]] (* Harvey P. Dale, Nov 04 2019 *)
PROG
(PARI) exp(2) - 2*exp(1) \\ Amiram Eldar, Jul 25 2026
CROSSREFS
KEYWORD
AUTHOR
Eric W. Weisstein, Dec 19 2003
STATUS
approved
