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A052111
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Number of self-complementary 2-multigraphs with loops on n nodes.
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2
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1, 2, 5, 24, 120, 956, 13214, 275848, 10613479, 601955190, 63788179593, 9985272721908, 2906903866536978, 1268802939666164781, 1023198355173637429689, 1258181815243248217067175, 2834890911778762731361375215, 9900896274205100008273760895560
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OFFSET
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1,2
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COMMENTS
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A 2-multigraph is similar to an ordinary graph except there are 0, 1 or 2 edges between any two nodes (self-loops are not allowed).
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LINKS
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PROG
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(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v) = {sum(i=2, #v, sum(j=1, i-1, if(v[i]*v[j]%2==0, gcd(v[i], v[j])))) + sum(i=1, #v, if(v[i]%2==0, v[i]\4*2+1))}
a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^edges(p)); s/n!} \\ Andrew Howroyd, Sep 16 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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