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A004115 Number of unlabeled rooted nonseparable graphs with n nodes.

%I A004115 M3592 #29 Nov 07 2021 15:28:17
%S A004115 0,1,1,4,22,178,2278,46380,1578060,92765486,9676866173,1821391854302,
%T A004115 625710416245358,395761853562201960,464128290507379386872,
%U A004115 1015085639712281997464676,4160440039279630394986003604,32088534920274236421098827156776
%N A004115 Number of unlabeled rooted nonseparable graphs with n nodes.
%D A004115 R. W. Robinson, personal communication.
%D A004115 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%D A004115 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A004115 Andrew Howroyd, <a href="/A004115/b004115.txt">Table of n, a(n) for n = 1..40</a> (terms 1..26 from R. W. Robinson)
%H A004115 R. W. Robinson, <a href="/A004115/a004115.pdf">Rooted non-separable graphs - computer printout</a>
%o A004115 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A004115 edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}
%o A004115 graphsCycleIndex(n)={my(s=0); forpart(p=n, s+=permcount(p) * 2^edges(p) * sMonomial(p)); s/n!}
%o A004115 graphsSeries(n)={sum(k=0, n, graphsCycleIndex(k)*x^k) + O(x*x^n)}
%o A004115 cycleIndexSeries(n)={my(g=graphsSeries(n), gcr=sPoint(g)/g); x*sSolve( sLog( gcr/(x*sv(1)) ), gcr )}
%o A004115 { my(N=15); Vec(OgfSeries(cycleIndexSeries(N)), -N) } \\ _Andrew Howroyd_, Dec 25 2020
%Y A004115 Cf. A002218, A007145, A013922.
%K A004115 nonn,nice
%O A004115 1,4
%A A004115 _N. J. A. Sloane_