Asymptotics of degrees of some S-n-sub regular representations

The numbers r(lambda) = Sigma(i greater than or equal to 1) d(lambda/(2,1)( 2i-1)), lambda proves n, appear in the enumeration of various objects, as w ell as coefficients in S-n representations associated with products of high er commutators. We study their asymptotics as n --> infinity and show that if (lambda(1), lambda(2), ...) approximate to (alpha(1), alpha(2), ...)n, i f (lambda'(1), lambda'(2),...) approximate to (beta(1), beta(2), ...)n and if gamma = 1 - Sigma(k greater than or equal to 1)(alpha(kappa) + beta(kapp a)), then [GRAPHICS]