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%I #9 Jun 11 2015 06:20:17
%S 3,9,53,231,5319,3167,1296273,1604979,64370707,22906587,411169704813,
%T 610433321,424312831956207,2146177886409,98731231639051,
%U 12218411169233691,1112291237880234922707,2196818399875253,2619031544578888560315813,16827894135040576041
%N Numerator of n + Sum(binomial(n,k)*(k/n)^k*((n-k)/n)^(n-k), k=0..n).
%H Helmut Prodinger, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p7/0">An identity conjectured by Lacasse via the tree function</a>, Electronic Journal of Combinatorics, 20(3) (2013), #P7. See xi_2(n).
%e 3, 9/2, 53/9, 231/32, 5319/625, 3167/324, 1296273/117649, 1604979/131072, ...
%o (PARI) a(n) = numerator(n + sum(k=0, n, binomial(n,k)*(k/n)^k*((n-k)/n)^(n-k))); \\ _Michel Marcus_, Jun 11 2015
%Y Denominators are in A036505. Cf. A090878, A063170.
%K nonn,frac
%O 1,1
%A _N. J. A. Sloane_, Jul 31 2013
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