A052114 Number of self-complementary directed 4-multigraphs with loops on n nodes.

1, 13, 313, 52891, 30554141, 89011081055, 1243751028948305, 70334570607769968970, 23735285427941643311618345, 27755772992017058140287194221448, 226477787759401129853705684271059207073, 5698414152656591747538959168064394745850705494

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..50

Prog

(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)*5^edges(p)); s/n!} \\ Andrew Howroyd, Sep 17 2018

Crossrefs

Cf. A052113, A053516, A053588.

Sequence in context: A241022 A331647 A331644 * A305143 A132485 A297437

Adjacent sequences: A052111 A052112 A052113 * A052115 A052116 A052117

Keyword

nonn

Author

Vladeta Jovovic, Jan 21 2000

Extensions

Terms a(11) and beyond from Andrew Howroyd, Sep 17 2018

Status

approved