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A295193 Number of regular simple graphs on n labeled nodes. 27
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)
OFFSET

1,2

LINKS

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

EXAMPLE

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

.

  4---1  3---1  2---1

  3---2  4---2  4---3

.

  3---4  4---3  4---2

  |   |  |   |  |   |

  1---2  1---2  1---3

.

  4---3

  | X |

  2---1

(End)

MATHEMATICA

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 *)

PROG

(PARI) \\ See link for program file.

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Álvar Ibeas, Nov 16 2017

EXTENSIONS

a(16)-a(18) from Andrew Howroyd, Aug 28 2019

STATUS

approved

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Last modified March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)