The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #17 Apr 29 2019 16:36:57
%S 1,0,1,1,28,448,18788,1419852,207249896,58206408344,31725488477648,
%T 33830818147141904,71068681534173472576,295648155633330113713344,
%U 2444510010072634827916776064,40269686339597630128483872278656,1323732128140903183968664175047409152
%N Number of point-labeled reduced two-graphs with n nodes.
%C Also number of (n-1)-node labeled mating graphs without isolated nodes, cf. A006024. - _Vladeta Jovovic_, Mar 23 2004
%H Michael De Vlieger, <a href="/A007833/b007833.txt">Table of n, a(n) for n = 1..83</a>
%H P. J. Cameron, <a href="http://www.combinatorics.org/Volume_2/volume2.html#R4">Counting two-graphs related to trees</a>, Elec. J. Combin., Vol. 2, #R4.
%F a(n) = Sum_{k=1..n} s(n, k) * 2^((k-1) * (k-2) / 2) where s(n, k) are the Stirling numbers of the first kind. - _Sean A. Irvine_, Feb 03 2018
%t Array[Sum[StirlingS1[#, k] 2^((k - 1) (k - 2)/2), {k, #}] &, 15] (* _Michael De Vlieger_, Feb 03 2018 *)
%Y Cf. A092430 (connected).
%K nonn
%O 1,5
%A _Peter J. Cameron_