A005642 -id:A005642 - cp's OEIS frontend

A123544 Number of connected labeled 2-regular relations of order n.

0, 0, 1, 6, 87, 1980, 66270, 3050460, 184716630, 14231775600, 1359481407480, 157694893448400, 21835679256606600, 3557942554594428000, 673941365091485290800, 146851484638349504613600

Offset: 0

N. J. A. Sloane, Nov 13 2006

nonn

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1982.

R. W. Robinson, Table of n, a(n) for n = 0..48

Connected version of A001499. Unlabeled version is A005642.

Cf. A123543.

m = 16;
a1499[n_] := (n - 1)*n!*Gamma[n - 1/2]*Hypergeometric1F1[2 - n, 3/2 - n, -1/2]/Sqrt[Pi];
egf = Log[1 + Sum[a1499[k] x^k/k!, {k, 1, m}]];
CoefficientList[egf + O[x]^m, x] Range[0, m-1]! (* Jean-François Alcover, Aug 26 2019 *)

seq(n)={Vec(serlaplace(log(serlaplace(exp(-x/2 + O(x*x^n))/sqrt(1-x + O(x*x^n))))), -(n+1))}; \\ Andrew Howroyd, Sep 09 2018

E.g.f.: log(1 + Sum_{k>0} A001499(k)*x^k/k!). - Andrew Howroyd, Sep 09 2018

A005641 Number of 2-diregular digraphs with n nodes.

Original entry on oeis.org

1, 3, 8, 27, 131, 711, 5055, 41607, 389759, 4065605, 46612528, 581713045, 7846380548, 113718755478, 1762208816647, 29073392136390, 508777045979418

Offset: 2

N. J. A. Sloane

nonn

These graphs may have loops, whereas A219889 does not admit them. Both sequences do not admit multiedges. - R. J. Mathar, Mar 27 2019

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Richard J. Mathar, 2-regular Digraphs of the Lovelock Lagrangian, arXiv:1903.12477 [math.GM], 2019.
M. V. S. Ramanath and T. R. Walsh, Enumeration and generation of a class of regular digraphs, J. Graph Theory 11 (1987), no. 4, 471-479. (Annotated scanned copy)

Cf. A005642 (inverse Euler transform, connected graphs).

A307155 Number of connected, loopless 2-regular digraphs, no multiedges, on n nodes.

Original entry on oeis.org

1, 0, 0, 1, 2, 5, 22, 90, 616, 4988, 46883, 493406, 5712809, 71909602

Offset: 0

R. J. Mathar, Mar 27 2019

nonn

Inverse Euler transform of A219889.
The Multiset Transform (number of loopless 2-regular digraphs on n nodes with c weakly connected components) of this sequence starts
in row 3 as:
1 ;
2 ;
5 ;
22 , 1 ;
90 , 2 ;
616 , 8 ;
4988 , 32 , 1 ;
46883 , 149 , 2 ;
493406 , 906 , 8 ;
5712809 , 6923 , 36 , 1 ;
71909602 , 61919 , 164 , 2 ;

Cf. A219889 (not necessarily connected), A005642 (loops admitted).

cp's OEIS Frontend

A123544 Number of connected labeled 2-regular relations of order n.

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A005641 Number of 2-diregular digraphs with n nodes.

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A307155 Number of connected, loopless 2-regular digraphs, no multiedges, on n nodes.

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