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%I #17 Sep 01 2018 09:22:34
%S 1,8,66,616,6530,77964,1037974,15266192,246003354,4312200340,
%T 81714050462,1664849747928,36296654286178,843235868819036,
%U 20797267023597030,542745686844469024,14942598078715420202,432842048921633654052,13159824571927634917678,419012563973742290424680
%N Total height of all elements in all preferential arrangements of n elements, where elements at the bottom level have height 1.
%H Alois P. Heinz, <a href="/A083385/b083385.txt">Table of n, a(n) for n = 1..200</a>
%H N. J. A. Sloane and Thomas Wieder, <a href="http://arXiv.org/abs/math.CO/0307064">The Number of Hierarchical Orderings</a>, Order 21 (2004), 83-89.
%F See A083384 for formula.
%F a(n) = A261781(n+1,n)/2. - _Alois P. Heinz_, Aug 10 2016
%F a(n) ~ n! * n^2 / (8 * (log(2))^(n+2)). - _Vaclav Kotesovec_, Jul 01 2018
%t a[n_] := n Sum[1/2 (k-1) k! StirlingS2[n, k], {k, 1, n}] + n Sum[(-1)^(k-j) Binomial[k, j] j^n, {j, 0, n}, {k, 0, n}];
%t Array[a, 20] (* _Jean-François Alcover_, Sep 01 2018 *)
%Y Equals A083384(n) + n*A000670(n).
%Y Cf. A000670, A083410, A261781.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jun 07 2003