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A052113
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Number of self-complementary directed 2-multigraphs with loops on n nodes.
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3
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1, 5, 41, 1023, 67173, 10771355, 5957216417, 6971880064072, 32181855124938673, 290910256437910060602, 11266525980714327353251353, 815201852317091835592374861144, 266236010885685869904935495261864265, 157899403462038839125137738939159318226008
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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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REFERENCES
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V. Jovovic, On the number of m-place relations (in Russian), Logiko-algebraicheskie konstruktsii, Tver, 1992, 59-66.
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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) = {2*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]))}
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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