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%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
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