\\ A320499: Number of connected self-dual signed graphs with n unlabeled 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}

\\ signed graph
A004102edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}
A004102(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^A004102edges(p)); s/n!}

\\ self dual signed graphs 
A004104edges(v) = {sum(i=2, #v, sum(j=1, i-1, if(v[i]*v[j]%2==0, gcd(v[i], v[j])))) + sum(i=1, #v, if(v[i]%2==0, v[i]\4*2))}
A004104(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^A004104edges(p)); s/n!}

\\ connected self dual signed graphs
A320499seq(n)={
  my(u=vector(n));
  my(v=InvEulerT(vector(n, i, A004104(i))));
  my(w=InvEulerT(vector(n\2, i, A004102(i))));
  for(i=1, #u, u[i] = v[i] - if(i%2==0, w[i/2]-u[i/2])/2);
  concat([1], u);
}