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

1, 2, 11, 52, 296, 1724, 11060, 74527, 533046, 3999187, 31412182, 257150093, 2188063401, 19299062896, 176059781439, 1657961491087, 16089088019098, 160643776819423, 1648068916722737, 17351137043998280, 187255329043638437, 2069426416836401375, 23397468305569068113, 270406562951254606048, 3191908298072118225550, 38454691427657997701136

Offset: 0

Author

Vladeta Jovovic, Jan 26 2000

Keywords

• nonn

Comments

Row sums of A136564, limiting values of A138107. - Benoit Jubin, May 13 2008

Euler transform of A137975. - M. F. Hasler, Jul 31 2017

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• Banglei Guan, Ji Zhao, and Laurent Kneip, Six-Point Method for Multi-Camera Systems with Reduced Solution Space, arXiv:2402.18066 [cs.CV], 2024. See p. 10.
• J.-C. Novelli, J.-Y. Thibon and N. M. Thiery, Algèbres de Hopf de graphes, C.R. Acad. Sci. Paris (Comptes Rendus Mathématique), 339 (2004), 607-610.
• Sanjaye Ramgoolam, Permutation Invariant Gaussian Matrix Models, arXiv:1809.07559 [hep-th], 2018.

Crossrefs

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

Cf. A104209. Cf. A137975 (connected).

Formula

a(n) = A138107(2*n,n). - Max Alekseyev, Oct 17 2017

Extensions

a(16)-a(25) from Max Alekseyev, Jun 21 2011