\\ A320994: Number of point-self-dual nets 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}

\\ nets (n nodes)
A004103edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}
A004103(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^A004103edges(p)*2^#p); s/n!}

\\ point-self dual nets (2n nodes)
A004105edges(v) = {sum(i=2, #v, sum(j=1, i-1, 2*gcd(v[i], v[j]))) + sum(i=1, #v, v[i])}
A004105(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^A004105edges(p)); s/n!}

\\ connected point-self dual nets (2n nodes)
A320994seq(n)={
  my(u=vector(n));
  my(v=InvEulerT(vector(n, i, A004105(i))));
  my(w=InvEulerT(vector(n, i, A004103(i))));
  for(i=1, #u, u[i] = v[i] - (w[i] - if(i%2==0, u[i/2]))/2);
  concat([1], u);
}