On the refined 3-enumeration of alternating sign matrices

An explicit expression for the numbers A(n,r;3) describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, A(n,r;3)'s are represented as 1-fold sums which can also be written in terms of terminating F34 series of argument 1/4.