(*第一个程序*)
nmax=19;
M=表[If[n==k,0,If[n==k+1,-n+1,-系数[(1-1/总和[i!*x^i,{i,0,n}])/x+O[x]^n,x,n-k-1]],{n,1,nmax+1},{k,1,nmax+1}];
温度[n_,k_]/;0<=k<=n:=和[(-1)^p矩阵幂[M,p][[n+1,k+1]]/p,{p,n+1}];T[_,_]=0;
a[n_]:=总和[T[n,k],{k,0,n}];
(*第二个节目*)
t[n,k]:=t[n,k]=If[n<k|k<0,0,If[n=k,1,If[n=k+1,n,k*t[n,k+1]+Sum[t[j,0]*t[n,j+k+1],{j,0,n-k-1}]]];
M: =M=带[{q=52},表[If[k>=n,0,t[n,k]],{n,0、q},{k,0,q}]];
f[j_]:=f[j]=矩阵幂[M,j];
T[n_,k_]:=T[n,k]=如果[k>n-1,0,和[(-1)^(j-1)*f[j][[n+1,k+1]]/j,{j,n}]];
a[n]:=a[n]=和[T[n,k],{k,0,n}];