On the enumeration of skew Young tableaux

For fixed n and a fixed partition α of k< n we give an explicit formula for the number N( n; α) of standard skew Young tableaux with n squares and shape λ/ α for some λ. From this formula the entire asymptotic expansion of N( n; α) as n→∞ can in principle be computed, generalizing recent work of McKay, Morse, and Wilf. We also give asymptotic formulas for the number f λ/ α of standard skew Young tableaux of shape λ/ α for α fixed and λ “large.”