A123543 Number of connected labeled 2-regular pseudodigraphs (multiple arcs and loops allowed) of order n.

0, 1, 2, 14, 201, 4704, 160890, 7538040, 462869190, 36055948320, 3474195588360, 405786523413600, 56502317464777800, 9248640671612865600, 1758505909558569771600, 384399253128691423022400

Offset

0,3

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} A000681(k)*x^k/k!). - Andrew Howroyd, Sep 09 2018

Mathematica

m = 16;
a681[n_] := n!*HypergeometricPFQ[{1/2, -n}, {}, -2]/2^n;
egf = Log[1 + Sum[a681[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 A000681.

First column of A307804.

Cf. A123544.

Sequence in context: A213977 A322196 A102224 * A279452 A262008 A054652

Adjacent sequences: A123540 A123541 A123542 * A123544 A123545 A123546

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2006

Status

approved