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A052151 Number of self-complementary directed 3-multigraphs on n nodes.

%I A052151 #11 Sep 12 2019 09:11:15
%S A052151 1,2,32,528,131328,22377984,91628068864,187650529822720,
%T A052151 12297831583666176000,322380224569805856440320,
%U A052151 338040160454396241027914530816,118153599638221082814732598131032064,1982288462105132553530631056140022239461376
%N A052151 Number of self-complementary directed 3-multigraphs on n nodes.
%H A052151 Andrew Howroyd, <a href="/A052151/b052151.txt">Table of n, a(n) for n = 1..50</a>
%t A052151 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];
%t A052151 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]}];
%t A052151 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!];
%t A052151 Array[a, 25] (* _Jean-François Alcover_, Sep 12 2019, after _Andrew Howroyd_ *)
%o A052151 (PARI)
%o A052151 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}
%o A052151 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)}
%o A052151 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
%Y A052151 Cf. A003086, A052112, A052152.
%K A052151 nonn
%O A052151 1,2
%A A052151 _Vladeta Jovovic_, Jan 24 2000
%E A052151 Terms a(13) and beyond from _Andrew Howroyd_, Sep 17 2018