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A052151
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Number of self-complementary directed 3-multigraphs on n nodes.
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1
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1, 2, 32, 528, 131328, 22377984, 91628068864, 187650529822720, 12297831583666176000, 322380224569805856440320, 338040160454396241027914530816, 118153599638221082814732598131032064, 1982288462105132553530631056140022239461376
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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permcount[v_List] := 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];
edges[v_List] := 4 Sum[Sum[GCD[v[[i]], v[[j]]], {j, 1, i - 1}], {i, 2, Length[v]}] + Sum[2 v[[i]] - 1, {i, 1, Length[v]}];
a[n_] := Module[{s = 0}, Do[s += permcount[2 p]*4^edges[p]*If[OddQ[n], n*16^Length[p], 1], {p, IntegerPartitions[Quotient[n, 2]]}]; s/n!];
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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) = {4*sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, 2*v[i]-1)}
a(n) = {my(s=0); forpart(p=n\2, s+=permcount(2*Vec(p))*4^edges(p)*if(n%2, n*16^#p, 1)); s/n!} \\ Andrew Howroyd, Sep 17 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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