  We give a proof of Awata and Yamada's conjecture for the explicit formula of
Whittaker vector of the deformed Virasoro algebra realized in the Fock space.
The formula is expressed as a summation over Macdonald symmetric functions with
factored coefficients. In the proof we fully use currents appearing in the Fock
representation of Ding-Iohara-Miki quantum algebra. We also mention an
interpretation of Whittaker vector in terms of the geometry of the Hilbert
schemes of points on the affine plane.
