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

1,1

Comments

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

Links

Table of n, a(n) for n=1..18.

Wikipedia, Regular graph

Gus Wiseman, The a(4) = 24 regular graphs with loops.

Gus Wiseman, The a(5) = 78 regular graphs with loops.

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}]

Prog

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

Crossrefs

Row sums of A333158.

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

Sequence in context: A230694 A155725 A103973 * A129826 A009296 A068554

Adjacent sequences: A322632 A322633 A322634 * A322636 A322637 A322638

Keyword

nonn

Author

Gus Wiseman, Dec 21 2018

Extensions

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

Status

approved