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

0,4

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

Formula

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

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 *)

Prog

(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

Crossrefs

Connected version of A001499. Unlabeled version is A005642.

Cf. A123543.

Sequence in context: A289394 A113666 A365011 * A239749 A277337 A138216

Adjacent sequences: A123541 A123542 A123543 * A123545 A123546 A123547

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2006

Status

approved