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A369290 Number of unlabeled simple graphs without endpoints with n edges.

%I A369290 #9 Feb 07 2024 23:27:44
%S A369290 1,0,0,1,1,2,6,10,25,68,182,538,1748,5935,21585,82904,334037,1406934,
%T A369290 6167455,28033776,131770437,638956188,3189940453,16369201031,
%U A369290 86214798929,465480395911,2573390342437,14553415319929,84118459655982,496514424803358,2990633679878654
%N A369290 Number of unlabeled simple graphs without endpoints with n edges.
%H A369290 Andrew Howroyd, <a href="/A369290/b369290.txt">Table of n, a(n) for n = 0..50</a>
%F A369290 Euler transform of A342556.
%o A369290 (PARI) \\ See also A369932 for a more efficient program.
%o A369290 permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
%o A369290 edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c-1)\2)*if(c%2, 1, t(c/2)))}
%o A369290 seq(n)={my(s=0); forpart(p=2*n, s+=permcount(p)*prod(i=1, #p, 1-x^p[i])*edges(p, w->1+x^w + O(x*x^n))); Vec(s/(2*n)!)}
%Y A369290 Row sums of A369932.
%Y A369290 Cf. A004110 (n vertices), A307316 (multigraph), A342556 (connected).
%K A369290 nonn
%O A369290 0,6
%A A369290 _Andrew Howroyd_, Jan 30 2024