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A007717 Number of symmetric polynomial functions of degree n of a symmetric matrix (of indefinitely large size) under joint row and column permutations. Also number of multigraphs with n edges (allowing loops) on an infinite set of nodes. 6
1, 2, 7, 23, 79, 274, 1003, 3763, 14723, 59663, 250738, 1090608, 4905430, 22777420, 109040012, 537401702, 2723210617, 14170838544, 75639280146, 413692111521, 2316122210804, 13261980807830, 77598959094772, 463626704130058, 2826406013488180, 17569700716557737 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Euler transform of A007719.

REFERENCES

Huaien Li and David C. Torney, Enumerations of Multigraphs, 2002.

LINKS

Table of n, a(n) for n=0..25.

Huaien Li and David C. Torney, Enumeration of unlabelled multigraphs, Ars Combin. 75 (2005) 171-188. MR2133219.

EXAMPLE

a(2) = 7 (here - denotes an edge, = denotes a pair of parallel edges and o is a loop):

oo

o o

o-

o -

=

--

- -

CROSSREFS

Cf. A050535, A002620, A007719, A050531, A050532, A053418, A053419, A000664, A052171.

Sequence in context: A068593 A198944 A112657 * A130567 A091514 A143629

Adjacent sequences:  A007714 A007715 A007716 * A007718 A007719 A007720

KEYWORD

nonn

AUTHOR

Colin Mallows

EXTENSIONS

More terms from Vladeta Jovovic, Jan 26 2000

a(0)=1 prepended and a(16)-a(25) added by Max Alekseyev, Jun 21 2011

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.