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%I #37 Jan 01 2023 04:29:08
%S 1,1,2,5,16,65,386,3700,55784,1134526,27053464
%N Maximal number of connected graphs of order n having distinct numbers of spanning trees.
%C a(n) grows asymptotically faster than sqrt(n)*exp(2*Pi*sqrt(n/log(n))/sqrt(3)).
%H Jernej Azarija, <a href="http://www.imfm.si/preprinti/PDF/01178.pdf">Counting graphs with different numbers of spanning trees through the counting of prime partitions</a> (preprint, 2012).
%H Jernej Azarija, <a href="http://mathoverflow.net/questions/100816/maximal-class-of-simple-graphs-of-order-n-with-mutually-distinct-numbers-of-spa">Maximal class of simple graphs of order n with mutually distinct number of spanning trees</a>, (Mathoverflow).
%H J. Sedlacek, <a href="http://dx.doi.org/10.21136/CPM.1969.117654">On the number of spanning trees of finite graphs</a>, Cas. Pro. Pest Mat., Vol. 94 (1969) 217-221.
%e a(3) = 2 since any connected graph on 3 vertices can either have 1 spanning tree (any tree) or 3 (triangle).
%o (Sage) # needs the package nauty:
%o len( set([g.spanning_trees_count() for g in graphs.nauty_geng('-c ' + str(n)) ]))
%K nonn,hard,more
%O 1,3
%A _Jernej Azarija_, Jun 27 2012
%E a(11) from _Jernej Azarija_, Sep 07 2012
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