A361254 Number of n-regular graphs on 2*n labeled nodes.

1, 1, 3, 70, 19355, 66462606, 2977635137862, 1803595358964773088, 15138592322753242235338875, 1793196665025885172290508971592750, 3040059281615704147007085764679679740691838, 74597015246986083384362428357508730776063716190667288, 26737694395324301026230134763403079891362936970900741153038680278

Offset

0,3

Comments

These graphs share the same degree sequence as the complete bipartite graphs K(n,n).

Links

Table of n, a(n) for n=0..12.

Atabey Kaygun, Counting Graphs with a Prescribed Degree Sequence

Atabey Kaygun, Enumerating Labeled Graphs that Realize a Fixed Degree Sequence, arXiv:2101.02299 [math.CO], 2021.

Formula

a(n) = A059441(2*n, n).

Prog

(Common Lisp) ; See Links in A339847 for the graph-count function.
(defun A361254 (n)
   (graph-count (loop repeat (* 2 n) collect n)))
(PARI) \\ See Links in A295193 for GraphsByDegreeSeq.
a(n)={if(n==0, 1, vecsum(GraphsByDegreeSeq(2*n, n, (p, r)->valuation(p, x) >= n-r)[, 2])) } \\ Andrew Howroyd, Mar 06 2023

Crossrefs

Cf. A001223, A059441, A339987, A360437.

Sequence in context: A210920 A140048 A135951 * A093245 A108231 A130894

Adjacent sequences: A361251 A361252 A361253 * A361255 A361256 A361257

Keyword

nonn

Author

Atabey Kaygun, Mar 06 2023

Extensions

a(11)-a(12) from Andrew Howroyd, Mar 06 2023

Status

approved