In this very well written paper, the author looks at the function \[ B(x,y,t)={{x-y}\over {xe^{-{{(x-y)}\over {2}}t}-ye^{{{(x-y)}\over {2}}t}}} \] for \(x\neq y\) and \(1/(1-xt)\) for \(x=y\). He shows that if \(c\) is any complex number then \[ B^c(x,y,t)=\sum_{n=0}^{\infty} 2^{-n} B_n(x,y,c) {{t^n}\over {n!}}, \] converges absolutely for \(| t| <| (\ln x-\ln y)/(x-y)| \), where \[ B_n(x,y,c)=\sum_{k=0}^n B_{n,k}(c)x^{n-k}y^k, \] and the coefficients \(B_{n,k}(c)\) satisfy the recurrence \[ B_{n+1,k+1}(c)=(2(k+1)+c)B_{n,k+1}(c)+(2(n-k)+c)B_{n,k}(c), \] with \(B_{0,0}(c)=1\) and \(B_{n,k}(c)=0\) if \(k>n\). The author also studies various properties of the numbers \(B_{n,k}(c)\). By specializing to certain particular values of the parameters, the author finds that the numbers \(B_{n,k}(c)\) are linked to Eulerian numbers, MacMahon numbers and Stirling numbers and he derives various new identities involving these numbers.