A369290 - OEIS

%I #9 Feb 07 2024 23:27:44

%S 1,0,0,1,1,2,6,10,25,68,182,538,1748,5935,21585,82904,334037,1406934,

%T 6167455,28033776,131770437,638956188,3189940453,16369201031,

%U 86214798929,465480395911,2573390342437,14553415319929,84118459655982,496514424803358,2990633679878654

%N Number of unlabeled simple graphs without endpoints with n edges.

%H Andrew Howroyd, <a href="/A369290/b369290.txt">Table of n, a(n) for n = 0..50</a>

%F Euler transform of A342556.

%o (PARI) \\ See also A369932 for a more efficient program.

%o 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 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 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 Row sums of A369932.

%Y Cf. A004110 (n vertices), A307316 (multigraph), A342556 (connected).

%K nonn

%O 0,6

%A _Andrew Howroyd_, Jan 30 2024