A322635 Number of regular graphs with loops on n labeled vertices.

2, 4, 4, 24, 78, 1908, 23368, 1961200, 75942758, 25703384940, 4184912454930, 4462909435830552, 2245354417775573206, 10567193418810168583576, 24001585002447984453495392, 348615956932626441906675011568, 2412972383955442904868321667433106, 162906453913051798826796439651249753404

Offset: 1

Author

Gus Wiseman, Dec 21 2018

Keywords

• nonn

Comments

A graph is regular if all vertices have the same degree. A loop adds 2 to the degree of its vertex.

Links

• Wikipedia, Regular graph
• Gus Wiseman, The a(4) = 24 regular graphs with loops.
• Gus Wiseman, The a(5) = 78 regular graphs with loops.

Crossrefs

Row sums of A333158.

Cf. A000666, A054921, A059441, A295193, A299353, A306017, A306021, A319189, A319190, A319612, A322659, A322661.

Programs

Mathematica

Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s,{s,Select[Tuples[Range[n],2],OrderedQ]}],Sequence@@Table[{x[i],0,k},{i,n}]],{k,0,2n}],{n,6}]

PARI

for(n=1, 10, print1(A322635(n), ", ")) \\ See A295193 for script, Andrew Howroyd, Aug 28 2019

Extensions

a(11)-a(18) from Andrew Howroyd, Aug 28 2019