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%I M4010 N1662 #44 Aug 04 2022 16:16:45
%S 1,5,52,1522,145984,48464496,56141454464,229148550030864,
%T 3333310786076963968,174695272746749919580928,
%U 33301710992539090379269318144,23278728241293494533015563325552128,60084295633556503802059558812644803074048,576025077880237078776946730871618386151571214336
%N Half the number of binary relations on n unlabeled points.
%D M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, pp. 14-22.
%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).
%H R. L. Davis, <a href="https://dx.doi.org/10.1090/S0002-9939-1953-0055294-2">The number of structures of finite relations</a>, Proc. Amer. Math. Soc. 4 (1953), 486-495.
%H M. D. McIlroy, <a href="/A000088/a000088.pdf">Calculation of numbers of structures of relations on finite sets</a>, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sep. 15, 1955, pp. 14-22. [Annotated scanned copy]
%H W. Oberschelp, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002298732">Kombinatorische Anzahlbestimmungen in Relationen</a>, Math. Ann., 174 (1967), 53-78.
%F a(n) = A000595(n)/2. - _Sean A. Irvine_, Mar 16 2012
%t permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
%t edges[v_] := Sum[2 GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total[v];
%t a[n_] := Module[{s = 0}, Do[s += permcount[p]*2^edges[p], {p, IntegerPartitions[n]}]; s/(2 n!)];
%t Array[a, 12] (* _Jean-François Alcover_, Aug 01 2019, after _Andrew Howroyd_ in A000595 *)
%Y Cf. A000595, A001174.
%K nonn,nice
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Apr 18 2000
%E a(13)-a(14) (based on A000595) from _Pontus von Brömssen_, Aug 04 2022
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