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%I #23 Sep 26 2023 17:03:21
%S 4,4,8,1,6,8,9,0,7,0,3,3,8,0,6,4,8,2,2,6,0,2,0,5,5,4,6,0,1,1,9,2,7,5,
%T 8,1,9,0,0,5,7,4,9,8,6,8,3,6,9,6,6,7,0,5,6,7,7,2,6,5,0,0,8,2,7,8,5,9,
%U 3,6,6,7,4,4,6,6,7,1,3,7,7,2,9,8,1,0,5,3,8,3,1,3,8,2,4,5,3,3,9,1,3,8,8,6,1
%N Decimal expansion of exp(3/2).
%C 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).
%H D. M. Bătinetu-Giurgiu, <a href="https://cms.math.ca/publications/crux/issue?volume=42&issue=8">Problem 4179</a>, Crux Mathematicorum, Vol. 42, No. 8 (2016), p. 357; <a href="https://cms.math.ca/publications/crux/issue?volume=43&issue=8">Solution to Problem 4179</a> by Kee-Wai Lau, ibid., Vol. 43, No. 8 (2017), p. 369.
%F Equals lim_{n->oo} n/A055209(n)^(1/n^2) (Bătinetu-Giurgiu, 2016). - _Amiram Eldar_, Apr 11 2022
%F Solution of x = Integral_{t=0..x} log(t^2) dt. - _Thomas Scheuerle_, Sep 22 2023
%e 4.4816890703380648226020554601192758190057498683696...
%t RealDigits[Exp[3/2],10,120][[1]] (* _Harvey P. Dale_, Apr 24 2016 *)
%Y Cf. A000142, A000166, A001113, A038205, A047865, A055209.
%K easy,nonn,cons
%O 1,1
%A _Alford Arnold_, Mar 10 2002
%E More terms from _Sascha Kurz_, Mar 19 2002
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