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A053419 Number of graphs with loops (symmetric relations) with n edges. 12
1, 2, 5, 14, 38, 107, 318, 972, 3111, 10410, 36371, 132656, 504636, 1998361, 8224448, 35112342, 155211522, 709123787, 3342875421, 16234342515, 81102926848, 416244824068, 2192018373522, 11831511359378, 65387590986455, 369661585869273, 2135966349269550, 12604385044890628 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second. a(n) is the number of non-isomorphic multiset partitions of {1, 1, 2, 2, 3, 3, ..., n, n} with no equivalent vertices. For example, non-isomorphic representatives of the a(2) = 5 multiset partitions are (1)(122), (11)(22), (1)(1)(22), (1)(2)(12), (1)(1)(2)(2). - Gus Wiseman, Jul 18 2018
a(n) is the number of unlabeled simple graphs with n edges rooted at one vertex. - Andrew Howroyd, Nov 22 2020
LINKS
FORMULA
Euler transform of A191970. - Andrew Howroyd, Oct 22 2019
MATHEMATICA
seq[n_] := Module[{A = O[x]^n}, G[2n, x+A, {1}] // CoefficientList[#, x]&]; (* Jean-François Alcover, Dec 03 2020, using Andrew Howroyd's code for g.f. G in A339063 *)
PROG
(PARI) \\ See A339063 for G.
seq(n)={my(A=O(x*x^n)); Vec(G(2*n, x+A, [1]))} \\ Andrew Howroyd, Nov 22 2020
CROSSREFS
Sequence in context: A052945 A026288 A006574 * A079227 A148314 A001011
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Jan 10 2000
EXTENSIONS
a(16)-a(24) from Max Alekseyev, Jan 22 2010
Terms a(25) and beyond from Andrew Howroyd, Oct 22 2019
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)