\\ A320993: Number of connected self-dual marked graphs on 2n nodes.
\\

InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v,n,polcoef(p,n)), vector(#v,n,1/n))}
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}


\\ marked graphs (n nodes)
A000666edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2 + 1)}
A000666(n) = {my(s=0); forpart(p=n, s+=permcount(p)*2^A000666edges(p)); s/n!}


\\ self-dual marked graphs (2n nodes)
A000595edges(v) = {sum(i=2, #v, sum(j=1, i-1, 2*gcd(v[i], v[j]))) + sum(i=1, #v, v[i])}
A000595(n) = {my(s=0); forpart(p=n, s+=permcount(p)*2^A000595edges(p)); s/n!}

\\ connected self-dual marked graphs (2n nodes)
A320993seq(n)={
  my(u=vector(n));
  my(v=InvEulerT(vector(n, i, A000595(i))));
  my(w=InvEulerT(vector(n, i, A000666(i))));
  for(i=1, #u, u[i] = v[i] - w[i]/2 + if(i%2==0, u[i/2]/2));
  concat([1], u)
}