If we weight instead by the Tutte polynomial. The case of spanning trees
> | Qtser:=proc(n) subs(q=(mu-1)*(nu-1), w=w/(nu-1), Qser(n)): end: |
> | map(normal,Qtser(3)); |
The case mu=nu=1 (spanning trees, cf beginning of section 11). We only count quasi-triangulations (no internal digon, x=0) with outer degree 2
> | m:=12:coeff(subs(mu=1, nu=1, z=1,x=0,t=1,map(normal,Qtser(m))),y,2); |
> | seq(binomial(2*n,n)*binomial(4*n-2,2*n-1)/2/n/(n+1),n=1..6); |
> | unassign('n'):simplify(normal(convert(asympt(binomial(2*n,n)*binomial(4*n-2,2*n-1)/2/n/(n+1),n,4),polynom))); |
> |