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A053419 Number of graphs with loops (symmetric relations) with n edges. 9
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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..50

FORMULA

Euler transform of A191970. - Andrew Howroyd, Oct 22 2019

CROSSREFS

Cf. A000664, A000666, A007716, A007717, A020555, A050535, A053419, A094574, A191970, A316974.

Sequence in context: A026288 A047086 A006574 * A079227 A148314 A001011

Adjacent sequences:  A053416 A053417 A053418 * A053420 A053421 A053422

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 February 23 06:42 EST 2020. Contains 332159 sequences. (Running on oeis4.)