A361254 - OEIS

%I #34 Mar 28 2023 15:29:48

%S 1,1,3,70,19355,66462606,2977635137862,1803595358964773088,

%T 15138592322753242235338875,1793196665025885172290508971592750,

%U 3040059281615704147007085764679679740691838,74597015246986083384362428357508730776063716190667288,26737694395324301026230134763403079891362936970900741153038680278

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

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

%H Atabey Kaygun, <a href="https://kaygun.tumblr.com/post/637867244800573440/counting-graphs-with-a-prescribed-degree-sequence">Counting Graphs with a Prescribed Degree Sequence</a>

%H Atabey Kaygun, <a href="https://arxiv.org/abs/2101.02299">Enumerating Labeled Graphs that Realize a Fixed Degree Sequence</a>, arXiv:2101.02299 [math.CO], 2021.

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

%o (Common Lisp) ; See Links in A339847 for the graph-count function.

%o (defun A361254 (n)

%o    (graph-count (loop repeat (* 2 n) collect n)))

%o (PARI) \\ See Links in A295193 for GraphsByDegreeSeq.

%o a(n)={if(n==0, 1, vecsum(GraphsByDegreeSeq(2*n, n, (p, r)->valuation(p,x) >= n-r)[, 2])) } \\ _Andrew Howroyd_, Mar 06 2023

%Y Cf. A001223, A059441, A339987, A360437.

%K nonn

%O 0,3

%A _Atabey Kaygun_, Mar 06 2023

%E a(11)-a(12) from _Andrew Howroyd_, Mar 06 2023