A083385 Total height of all elements in all preferential arrangements of n elements, where elements at the bottom level have height 1.

1, 8, 66, 616, 6530, 77964, 1037974, 15266192, 246003354, 4312200340, 81714050462, 1664849747928, 36296654286178, 843235868819036, 20797267023597030, 542745686844469024, 14942598078715420202, 432842048921633654052, 13159824571927634917678, 419012563973742290424680

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