OFFSET
1,2
COMMENTS
Average length of the first increasing run in a random permutation of n integers as n->Infinity.
Engel expansion of number e - 1 is sequence of natural numbers (A000027). - Jaroslav Krizek, Jan 23 2014
LINKS
Eric Weisstein's World of Mathematics, Permutation
FORMULA
Sum_{k >= 1} 1/k!. - Eric Desbiaux, Mar 21 2009
Equals Sum_{k>=1} H(k)*(k-1)/k!, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Aug 19 2020
EXAMPLE
e - 1 = 1.71828182...
MATHEMATICA
RealDigits[N[E - 1, 105]][[1]]
PROG
(PARI) exp(1) - 1 \\ Michel Marcus, Aug 07 2019
CROSSREFS
KEYWORD
AUTHOR
Eric W. Weisstein, Dec 19 2003
STATUS
approved