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A052171 Number of directed multigraphs with loops on an infinite set of nodes containing a total of n arcs. 9

%I #35 Mar 04 2024 15:18:27

%S 1,2,11,52,296,1724,11060,74527,533046,3999187,31412182,257150093,

%T 2188063401,19299062896,176059781439,1657961491087,16089088019098,

%U 160643776819423,1648068916722737,17351137043998280,187255329043638437,2069426416836401375,23397468305569068113,270406562951254606048,3191908298072118225550,38454691427657997701136

%N Number of directed multigraphs with loops on an infinite set of nodes containing a total of n arcs.

%C Row sums of A136564, limiting values of A138107. - _Benoit Jubin_, May 13 2008

%C Euler transform of A137975. - _M. F. Hasler_, Jul 31 2017

%H Andrew Howroyd, <a href="/A052171/b052171.txt">Table of n, a(n) for n = 0..50</a>

%H Banglei Guan, Ji Zhao, and Laurent Kneip, <a href="https://arxiv.org/abs/2402.18066">Six-Point Method for Multi-Camera Systems with Reduced Solution Space</a>, arXiv:2402.18066 [cs.CV], 2024. See p. 10.

%H J.-C. Novelli, J.-Y. Thibon and N. M. Thiery, <a href="http://nicolas.thiery.name/Preprints/NovelliThibonThiery.2004/NovelliThibonThiery.2004.pdf">Algèbres de Hopf de graphes</a>, C.R. Acad. Sci. Paris (Comptes Rendus Mathématique), 339 (2004), 607-610.

%H Sanjaye Ramgoolam, <a href="https://arxiv.org/abs/1809.07559">Permutation Invariant Gaussian Matrix Models</a>, arXiv:1809.07559 [hep-th], 2018.

%F a(n) = A138107(2*n,n). - _Max Alekseyev_, Oct 17 2017

%Y Cf. A050535, A007717, A005993, A050927, A050929.

%Y Cf. A104209. Cf. A137975 (connected).

%K nonn

%O 0,2

%A _Vladeta Jovovic_, Jan 26 2000

%E a(16)-a(25) from _Max Alekseyev_, Jun 21 2011

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Last modified April 23 16:40 EDT 2024. Contains 371916 sequences. (Running on oeis4.)