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 A083385 Total height of all elements in all preferential arrangements of n elements, where elements at the bottom level have height 1. 4
 1, 8, 66, 616, 6530, 77964, 1037974, 15266192, 246003354, 4312200340, 81714050462, 1664849747928, 36296654286178, 843235868819036, 20797267023597030, 542745686844469024, 14942598078715420202, 432842048921633654052, 13159824571927634917678, 419012563973742290424680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..200 N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89. FORMULA See A083384 for formula. a(n) = A261781(n+1,n)/2. - Alois P. Heinz, Aug 10 2016 a(n) ~ n! * n^2 / (8 * (log(2))^(n+2)). - Vaclav Kotesovec, Jul 01 2018 MATHEMATICA 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}]; Array[a, 20] (* Jean-François Alcover, Sep 01 2018 *) CROSSREFS Equals A083384(n) + n*A000670(n). Cf. A000670, A083410, A261781. Sequence in context: A121777 A056621 A152275 * A275230 A188450 A121766 Adjacent sequences:  A083382 A083383 A083384 * A083386 A083387 A083388 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 07 2003 STATUS approved

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Last modified September 19 13:13 EDT 2020. Contains 337178 sequences. (Running on oeis4.)