A193130 - OEIS

%I #17 Mar 18 2021 08:24:34

%S 0,4,384,82944,32768000,20736000000,19271206305792,24759631762948096,

%T 42071440246337175552,91403961001574400000000,

%U 247248735803801600000000000,815050629127324260701847945216,3217014140995401936351315753959424

%N Numbers of spanning trees of the cocktail party graphs.

%C Number of trees on 2n labeled vertices containing no edges from a prescribed perfect matching. - _Joel B. Lewis_, Jun 20 2013

%D Dragoš M. Cvetković, Michael Doob, Horst Sachs, Spectra of Graphs: Theory and Application, Academic Press, 1980.

%H Takashi Horiyama, Masahiro Miyasaka, Riku Sasaki, <a href="https://www.cs.umanitoba.ca/~cccg2018/papers/session7B-p2.pdf">Isomorphism Elimination by Zero-Suppressed Binary Decision Diagrams</a>, 30th Canadian Conference on Computational Geometry, 2018. See Table 2.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>

%F a(n) = n^(n-2) * (n-1)^n * 4^(n-1). [See "Spectra of graphs", p. 217; also observed by _Joel B. Lewis_, Jun 20 2013] - _Andrey Zabolotskiy_, Mar 18 2021

%Y Cf. A091159 (up to isomorphism).

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Jul 16 2011