A123543 - OEIS

%I #14 Aug 26 2019 08:37:01

%S 0,1,2,14,201,4704,160890,7538040,462869190,36055948320,3474195588360,

%T 405786523413600,56502317464777800,9248640671612865600,

%U 1758505909558569771600,384399253128691423022400

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

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

%H R. W. Robinson, <a href="/A123543/b123543.txt">Table of n, a(n) for n = 0..48</a>

%F E.g.f.: log(1 + Sum_{k>0} A000681(k)*x^k/k!). - _Andrew Howroyd_, Sep 09 2018

%t m = 16;

%t a681[n_] := n!*HypergeometricPFQ[{1/2, -n}, {}, -2]/2^n;

%t egf = Log[1 + Sum[a681[k] x^k/k!, {k, 1, m}]];

%t CoefficientList[egf + O[x]^m, x] Range[0, m-1]! (* _Jean-François Alcover_, Aug 26 2019 *)

%o (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

%Y Connected version of A000681.

%Y First column of A307804.

%Y Cf. A123544.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Nov 13 2006