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%I M1655 N0648 #43 Dec 24 2021 00:34:03
%S 1,1,2,6,21,94,512,3485,29515,314474,4255727,73831813,1653083021,
%T 47941962135,1803010446411,87882300251730,5543501326580737
%N Number of connected topologies with n unlabeled nodes.
%D K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D J. A. Wright, There are 718 6-point topologies, quasi-orderings and transgraphs, Notices Amer. Math. Soc., 17 (1970), p. 646, Abstract #70T-A106.
%D J. A. Wright, personal communication.
%H K. K.-H. Butler and G. Markowsky, <a href="http://www.laptop.maine.edu/Enumeration.pdf">Enumeration of finite topologies</a>, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184
%H K. K.-H. Butler and G. Markowsky, <a href="/A000798/a000798_1.pdf">Enumeration of finite topologies</a>, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184. [Annotated scan of pages 180 and 183 only]
%H P. J. Cameron, <a href="https://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 Henry Sharp, Jr., <a href="/A001930/a001930_1.pdf">Quasi-orderings and topologies on finite sets</a>, Proceedings of the American Mathematical Society 17.6 (1966): 1344-1349. [Annotated scanned copy]
%H N. J. A. Sloane, <a href="/A000112/a000112_2.pdf">List of sequences related to partial orders, circa 1972</a>
%H J. A. Wright, <a href="/A000798/a000798_3.pdf">There are 718 6-point topologies, quasiorderings and transgraphs</a>, Preprint, 1970 [Annotated scanned copy]
%H J. A. Wright, <a href="/A000798/a000798_4.pdf">Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences</a>
%F Inverse Euler transform of A001930. - _Vladeta Jovovic_, Jan 06 2006
%t A001930 = Cases[Import["https://oeis.org/A001930/b001930.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerInvTransform is defined in A022562 *)
%t {1} ~Join~ EulerInvTransform[Rest[A001930]] (* _Jean-François Alcover_, Jan 01 2020, updated Mar 17 2020 *)
%Y Cf. A001929, A001930.
%K nonn,more
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Jan 06 2006