A123544 - OEIS

%I #15 May 11 2022 12:11:59

%S 0,0,1,6,87,1980,66270,3050460,184716630,14231775600,1359481407480,

%T 157694893448400,21835679256606600,3557942554594428000,

%U 673941365091485290800,146851484638349504613600

%N Number of connected labeled 2-regular relations 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="/A123544/b123544.txt">Table of n, a(n) for n = 0..48</a>

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

%t m = 16;

%t a1499[n_] := (n - 1)*n!*Gamma[n - 1/2]*Hypergeometric1F1[2 - n, 3/2 - n, -1/2]/Sqrt[Pi];

%t egf = Log[1 + Sum[a1499[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 A001499. Unlabeled version is A005642.

%Y Cf. A123543.

%K nonn

%O 0,4

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