Mortici (2015) [31] proposed a new formula for approximating the gamma function and the convergence of the corresponding asymptotic series is very fast in comparison with other classical or recently discovered asymptotic series. In this paper, by the Lagrange–Bürmann formula we give an explicit formula for determining the coefficients ak (k=1,2,…) in Mortici's formula such thatΓ(x+1)2πx(xe)x∼exp{∑k=1∞ak(x12x2+25)k},x→∞. Moreover, by the cycle indicator polynomial of symmetric group, we give an explicit expression for the coefficients bk (k=0,1,…) of the following expansion:Γ(x+1)2πx(xe)x∼(∑k=0∞bk(x12x2+25)k)1/r,x→∞. A recursive formula for calculating the coefficients bk (k=0,1,…) is also given.