Coefficients in some Young Derived Sequences

Letηq={ηrqn}n≥0denote theSncharacter sequence obtained fromηby aq-column dilation of the Young diagrams, and letyl(ηq)denote itslth Young derived sequence [7]. We prove a formula expressing the coefficients inyl(ηq)in terms of those inηand of semistandard tableaux. The asymptotics of these sequences yield new extensions of the Mehta integral.