(PARI)
Q(n,k)={\\c-有n条边,k个顶点的网
如果(k<2+(n+2)\3|k>2*n\3,返回(0));
sum(i=2,k,sum(j=k,n,(-1)^((i+j+1-k)%2)*二项式(i+j-k,i)*i*(i-1)/2*
(二项式(2*n-2*k+2,k-i)*二项式-
4*二项式(2*n-2*k+1,k-i-1)*二项法(2*k-3,n-j-1));
};
我的(x='x+O('x^(3*N+1)),t=t+O(t^(N+4)),
q=t*x*Ser(向量(3*N+1,N,Polrev(向量(min(N+3,2*N\3),k,q(N,k)),'t)),
d=serreverse((1+x)/exp(q/(2*t^2*x)+t*x^2/(1+t*x))-1),
g2=整数(t^2/2*((1+d)/(1+x)-1));
serlaplace(Ser(向量(N,N,subst(polceoff(g2,N,'t),'x,'t,)))*'x);
};