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%I M2868 N1153 #26 Jan 17 2020 09:32:08
%S 1,3,10,45,272,2548,39632,1104306,56871880,5463113568,978181717680,
%T 326167542296048,202701136710498400,235284321080559981952,
%U 511531711735594715527360,2089424601541011618029114896,16084004145036771186002041099712,234026948449058790311618594954430848,6454432593140577452393525511509194184320
%N Number of symmetric reflexive relations on n nodes: (1/2)*A000666.
%D Harary, Frank; Palmer, Edgar M.; Robinson, Robert W.; Schwenk, Allen J.; Enumeration of graphs with signed points and lines. J. Graph Theory 1 (1977), no. 4, 295-308.
%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 W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
%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 Jean-François Alcover, <a href="/A000250/b000250.txt">Table of n, a(n) for n = 1..40</a>
%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]
%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[Sum[GCD[v[[i]], v[[j]]], {j, 1, i - 1}], {i, 2, Length[v]} ] + Sum[Quotient[v[[i]], 2] + 1, {i, 1, Length[v]}];
%t a[n_] := Module[{s = 0}, Do[s += permcount[p]*2^edges[p], {p, IntegerPartitions[n]}]; s/(2 n!)];
%t a /@ Range[19] (* _Jean-François Alcover_, Jan 17 2020, after _Andrew Howroyd_ in A000666 *)
%Y Cf. A000595, A001173, A001174.
%K nonn,nice
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Apr 18 2000
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007
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