OFFSET
1,1
COMMENTS
It is well known that derangements, A000166, are related to exp(1) (cf. A001113). It appears that derangements with minimal cycle size 3 relate to exp(1+1/2). for example, 720/160 = 4.5, 5040/1140 = 4.4210, 40320/8988 = 4.4859, 362880/80864 = 4.4875 the pattern continues - derangements with minimal cycle size 4 appear to relate in the same way to exp(1 + 1/2 +1/3).
LINKS
D. M. Bătinetu-Giurgiu, Problem 4179, Crux Mathematicorum, Vol. 42, No. 8 (2016), p. 357; Solution to Problem 4179 by Kee-Wai Lau, ibid., Vol. 43, No. 8 (2017), p. 369.
FORMULA
Equals lim_{n->oo} n/A055209(n)^(1/n^2) (Bătinetu-Giurgiu, 2016). - Amiram Eldar, Apr 11 2022
Solution of x = Integral_{t=0..x} log(t^2) dt. - Thomas Scheuerle, Sep 22 2023
EXAMPLE
4.4816890703380648226020554601192758190057498683696...
MATHEMATICA
RealDigits[Exp[3/2], 10, 120][[1]] (* Harvey P. Dale, Apr 24 2016 *)
CROSSREFS
KEYWORD
AUTHOR
Alford Arnold, Mar 10 2002
EXTENSIONS
More terms from Sascha Kurz, Mar 19 2002
STATUS
approved