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A295193
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Number of regular simple graphs on n labeled nodes.
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27
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1, 2, 2, 8, 14, 172, 932, 45936, 1084414, 155862512, 10382960972, 6939278572096, 2203360500122300, 4186526756621772344, 3747344008241368443820, 35041787059691023579970848, 156277111373303386104606663422, 4142122641757598618318165240180096
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..20
E. A. Bender and E. R. Canfield, The asymptotic number of labeled graphs with given degree sequences, Journal of Combinatorial Theory, Series A, 24 (1978), 296-307.
Andrew Howroyd, PARI Program
B. D. McKay, Applications of a technique for labelled enumeration, Congress. Numerantium, 40 (1983), 207-221.
Wikipedia, Regular graph
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EXAMPLE
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From Gus Wiseman, Dec 19 2018: (Start)
A graph is regular if all vertices have the same degree. For example, the a(4) = 8 simple regular graphs are:
1 2
3 4
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4---1 3---1 2---1
3---2 4---2 4---3
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3---4 4---3 4---2
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1---2 1---2 1---3
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4---3
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2---1
(End)
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MATHEMATICA
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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 *)
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PROG
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(PARI) \\ See link for program file.
for(n=1, 10, print1(A295193(n), ", ")) \\ Andrew Howroyd, Aug 28 2019
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CROSSREFS
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Row sums of A059441.
Cf. A005176 (unlabeled equivalent), A058891, A116539, A299353, A306017, A306021, A319189, A319190, A319612, A319729.
Sequence in context: A228661 A026585 A229730 * A248097 A098273 A220172
Adjacent sequences: A295190 A295191 A295192 * A295194 A295195 A295196
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KEYWORD
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nonn
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AUTHOR
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Álvar Ibeas, Nov 16 2017
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EXTENSIONS
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a(16)-a(18) from Andrew Howroyd, Aug 28 2019
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STATUS
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approved
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