%I #9 Sep 17 2018 15:41:05

%S 1,13,313,52891,30554141,89011081055,1243751028948305,

%T 70334570607769968970,23735285427941643311618345,

%U 27755772992017058140287194221448,226477787759401129853705684271059207073,5698414152656591747538959168064394745850705494

%N Number of self-complementary directed 4-multigraphs with loops on n nodes.

%H Andrew Howroyd, <a href="/A052114/b052114.txt">Table of n, a(n) for n = 1..50</a>

%o (PARI)

%o 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 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]))}

%o a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*5^edges(p)); s/n!} \\ _Andrew Howroyd_, Sep 17 2018

%Y Cf. A052113, A053516, A053588.

%K nonn

%O 1,2

%A _Vladeta Jovovic_, Jan 21 2000

%E Terms a(11) and beyond from _Andrew Howroyd_, Sep 17 2018