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A295193 Number of regular simple graphs on n labeled nodes.

%I A295193 #36 Apr 22 2021 17:56:47
%S A295193 1,2,2,8,14,172,932,45936,1084414,155862512,10382960972,6939278572096,
%T A295193 2203360500122300,4186526756621772344,3747344008241368443820,
%U A295193 35041787059691023579970848,156277111373303386104606663422,4142122641757598618318165240180096
%N A295193 Number of regular simple graphs on n labeled nodes.
%H A295193 Andrew Howroyd, <a href="/A295193/b295193.txt">Table of n, a(n) for n = 1..24</a>
%H A295193 E. A. Bender and E. R. Canfield, <a href="https://doi.org/10.1016/0097-3165(78)90059-6">The asymptotic number of labeled graphs with given degree sequences</a>, Journal of Combinatorial Theory, Series A, 24 (1978), 296-307.
%H A295193 Andrew Howroyd, <a href="/A295193/a295193.txt">PARI Program</a>
%H A295193 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.
%H A295193 B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/papers/LabelledEnumeration.pdf">Applications of a technique for labelled enumeration</a>, Congress. Numerantium, 40 (1983), 207-221.
%H A295193 Wikipedia, <a href="https://en.wikipedia.org/wiki/Regular_graph">Regular graph</a>
%e A295193 From _Gus Wiseman_, Dec 19 2018: (Start)
%e A295193 A graph is regular if all vertices have the same degree. For example, the a(4) = 8 simple regular graphs are:
%e A295193   1 2
%e A295193   3 4
%e A295193 .
%e A295193   4---1  3---1  2---1
%e A295193   3---2  4---2  4---3
%e A295193 .
%e A295193   3---4  4---3  4---2
%e A295193   |   |  |   |  |   |
%e A295193   1---2  1---2  1---3
%e A295193 .
%e A295193   4---3
%e A295193   | X |
%e A295193   2---1
%e A295193 (End)
%t A295193 Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s,{s,Subsets[Range[n],{2}]}],Sequence@@Table[{x[i],0,k},{i,n}]],{k,0,n-1}],{n,1,9}] (* _Gus Wiseman_, Dec 19 2018 *)
%o A295193 (PARI) \\ See link for program file.
%o A295193 for(n=1, 10, print1(A295193(n), ", ")) \\ _Andrew Howroyd_, Aug 28 2019
%Y A295193 Row sums of A059441.
%Y A295193 Cf. A005176 (unlabeled equivalent), A058891, A116539, A299353, A306017, A306021, A319189, A319190, A319612, A319729.
%K A295193 nonn
%O A295193 1,2
%A A295193 _Álvar Ibeas_, Nov 16 2017
%E A295193 a(16)-a(18) from _Andrew Howroyd_, Aug 28 2019