A138352
Table read by antidiagonals: T(n,k) is the number of transitive directed multigraphs with loops with n arcs and k vertices.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 5, 1, 0, 1, 2, 8, 8, 1, 0, 1, 2, 9, 20, 14, 1, 0, 1, 2, 9, 29
Offset: 0
Original entry on oeis.org
1, 4, 22, 111, 570, 2917, 15112, 78900, 416525, 2221529, 11974498, 65211746, 358742016, 1992975905, 11178149883, 63279615534, 361464920864, 2082869242399, 12104344580384, 70924864962233, 418922049779244
Offset: 0
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\\ Needs G function from A138107.
a(n)={if(n==0, 1, my(m=2*n); polcoef(G(3*n, x + O(x*x^m)) - G(3*n-1, x + O(x*x^m)), m))} \\ Andrew Howroyd, Apr 20 2020
A362387
Number of directed multigraphs including self-loops on n vertices and n edges.
Original entry on oeis.org
1, 1, 6, 31, 198, 1270, 8838, 63419, 475796, 3697876, 29793899, 248312750, 2139071800, 19023864211, 174495408060, 1648972635108, 16036927429350, 160338342813918, 1646265278973845, 17340402062779049, 187190960572134321
Offset: 0
For n=2 we have two edges and two vertices, for a total of six graphs:
* one vertex with two loops attached to it
* one loop attached to each vertex
* two vertices linked by two edges in opposite directions
* two vertices linked by two edges in the same direction
* one vertex with a loop being pointed at
* one vertex with a loop being pointed away from.
- F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973, page 88.
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