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

Author

N. J. A. Sloane, Nov 13 2006

Keywords

• nonn

References

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

Links

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

Crossrefs

Connected version of A001499. Unlabeled version is A005642.

Cf. A123543.

Programs

Mathematica

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 *)

PARI

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

Formula

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