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%I M3121 #30 Aug 27 2019 10:43:56
%S 1,0,1,3,29,2101,7011181,1788775603301,53304526022885278403,
%T 366299663378889804782330207902,
%U 1171638318502622784366970315262493034215728,3517726593606524901243694560022510194169866584119717555335
%N Number of connected 2-plexes.
%C The Palmer reference (incorrectly) has a(7)=7011349, a(8)=1788775603133, a(9)=53304526022885278659. - _Sean A. Irvine_, Mar 05 2015
%C Also connected 3-uniform hypergraphs on n vertices. - _Gus Wiseman_, Feb 23 2019
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H E. M. Palmer, <a href="http://dx.doi.org/10.1016/0012-365X(73)90069-1">On the number of n-plexes</a>, Discrete Math., 6 (1973), 377-390.
%F Inverse Euler transform of A000665. - _Sean A. Irvine_, Mar 05 2015
%e From _Gus Wiseman_, Feb 23 2019: (Start)
%e Non-isomorphic representatives of the a(5) = 29 2-plexes:
%e {{125}{345}}
%e {{123}{245}{345}}
%e {{135}{245}{345}}
%e {{145}{245}{345}}
%e {{123}{145}{245}{345}}
%e {{124}{135}{245}{345}}
%e {{125}{135}{245}{345}}
%e {{134}{235}{245}{345}}
%e {{145}{235}{245}{345}}
%e {{123}{124}{135}{245}{345}}
%e {{123}{145}{235}{245}{345}}
%e {{124}{134}{235}{245}{345}}
%e {{134}{145}{235}{245}{345}}
%e {{135}{145}{235}{245}{345}}
%e {{145}{234}{235}{245}{345}}
%e {{123}{124}{134}{235}{245}{345}}
%e {{123}{134}{145}{235}{245}{345}}
%e {{123}{145}{234}{235}{245}{345}}
%e {{124}{135}{145}{235}{245}{345}}
%e {{125}{135}{145}{235}{245}{345}}
%e {{135}{145}{234}{235}{245}{345}}
%e {{123}{124}{135}{145}{235}{245}{345}}
%e {{124}{135}{145}{234}{235}{245}{345}}
%e {{125}{135}{145}{234}{235}{245}{345}}
%e {{134}{135}{145}{234}{235}{245}{345}}
%e {{123}{124}{135}{145}{234}{235}{245}{345}}
%e {{125}{134}{135}{145}{234}{235}{245}{345}}
%e {{124}{125}{134}{135}{145}{234}{235}{245}{345}}
%e {{123}{124}{125}{134}{135}{145}{234}{235}{245}{345}}
%e (End)
%Y Column k=3 of A301924.
%Y Cf. A000665 (unlabeled 3-uniform), A025035, A125791 (labeled 3-uniform), A289837, A301922, A302374 (labeled 3-uniform spanning), A302394, A306017, A319540, A320395, A322451 (unlabeled 3-uniform spanning), A323292-A323299.
%K nonn,nice
%O 1,4
%A _N. J. A. Sloane_
%E a(7)-a(9) corrected and extended by _Sean A. Irvine_, Mar 05 2015
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