The General Form of the Accurate Formula of A(n,k)

Let A(n,k) denote the number of non-negative integer solutions of Diophantine equation (∑ki=1)ix_i=n. In this paper, the authors find the general form of the general solutions of the recurrent formula A(n,k)=A(n,k-1)+A(n-k,k), which is A(n,k)=(∑km=1)(∑mr=1)(∑[k/m]-1j=0)t~((k))_(m,r,j)×n~j×s(r,m)×ζ~(nr)_m, where ζ_m=e~(2πi/m), and s(r,m)=1,gcd(r,m)=1, 0,others.