VanInverse(B)

function A = VanInverse(B)
% This function inverse a Vandermonde Matrix B. 
% Matrix B is a n-by-n matrix, its (i,j) entry is i^(j-1),
% where i,j = 1,2,...,n
% for example, n = 4
% B =
%     1     1     1     1
%     1     2     4     8
%     1     3     9    27
%     1     4    16    64
% This routine uses a Stirling polynomial(the first kind) coefficients
% For fast operation, a C Stirling coefficient function has
% been posted with name: mStirling.c. The C-version of this 
% inverse function is also available upon request.

n = size(B,1);
A = zeros(n,n);

% compute the Stirling coeffs (by column), could use mStirling.c
for (i=1:n)
   if (i==1) 
       k = 3;
       coeff = [1 -2];
   else
       k = 2;
       coeff = [1 -1];
   end
   while (k<=n)
       if (k == i);
           k = k + 1;
            continue;
        else
            coeff = conv(coeff, [1 -k]);
            k = k + 1;
        end
    end
    A(:,i) = coeff' .* ((-1).^(n-i)/(factorial(n-i)*factorial(i-1)));
end

A = flipud(A);