\\ A320491: Number of connected edge-self-dual nets with n 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 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!} \\ edge-self-dual nets A004106edges(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))} A004106(n) = {my(s=0); forpart(p=n, s+=permcount(p)*3^A004106edges(p)*2^#p); s/n!} \\ connected edge-self-dual nets A320491seq(n)={ my(u=vector(n)); my(v=InvEulerT(vector(n, i, A004106(i)))); my(w=InvEulerT(vector(n\2, i, A004103(i)))); for(i=1, #u, u[i] = v[i] - if(i%2==0, w[i/2]-u[i/2])/2); concat([1], u); }