Pade approximant related to the Wallis formula

Based on the Pade approximation method, in this paper we determine the coefficients a(j) and b(j) such that pi = ((2n)!!/(2n - 1)!!)(2) {n(k) + a(1)n(k-1) + ... + a(k)/n(k+1) + b(1)n(k) + ... + b(k+1) + O(1/n(2k+3))}, n -> infinity, where k >= 0 is any given integer. Based on the obtained result, we establish a more accurate formula for approximating pi, which refines some known results.