
PROG

(PARI) {a(n)=local(M=Mat(1), N, L=Mat(1), C=matrix(n+2, n+2, r, c, if(r==c, 1, if(r==c+1, c)))); for(i=1, n+1, N=M; M=matrix(#N+1, #N+1, r, c, if(r>=c, if(r<=#N, (N^(#N))[r, c], (C^((#M)^2))[r, c]))); L=sum(i=1, #M, (M^0M)^i/i); M=sum(i=0, #M, (L/#N)^i/i!); ); L[n+1, 1]/(n+1)}
