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a(n) is the number of regular D classes in the semigroup of all binary relations on [n].
1

%I #21 Jun 12 2022 16:14:14

%S 1,2,4,9,25,88,406,2451,19450,202681,2769965,49519392,1154411138,

%T 34978238590,1373171398361,69648249299517,4552778914494604

%N a(n) is the number of regular D classes in the semigroup of all binary relations on [n].

%C Previous name was: Partial sums of A000112.

%H K. K.-H. Butler and G. Markowsky, <a href="https://www.koreascience.or.kr/article/JAKO197225748110925.pdf">The Number of Maximal Subgroups of the Semigroup of Binary Relations</a>, Kyungpook Math. J. Vol 12, June 1972.

%F a(n) = Sum_{i=0..n} A000112(i).

%t Cases[Import["https://oeis.org/A000112/b000112.txt", "Table"], {_, _}][[All, 2]] // Accumulate (* _Jean-François Alcover_, Jan 01 2020 *)

%Y Cf. A000112, A000798 (labeled topologies), A001035 (labeled posets), A001930 (unlabeled topologies), A006057, A079263, A079265, A007903.

%K nonn,hard,more

%O 0,2

%A _Jonathan Vos Post_, Feb 16 2010

%E New name from _Geoffrey Critzer_, May 22 2022