  We consider the semilinear Lane-Emden problem in a smooth bounded domain of
the plane. The aim of the paper is to analyze the asymptotic behavior of sign
changing solutions as the exponent p of the nonlinearity goes to infinity.
Among other results we show, under some symmetry assumptions on the domain,
that the positive and negative parts of a family of symmetric solutions
concentrate at the same point, as p goes to infinity, and the limit profile
looks like a tower of two bubbles given by a superposition of a regular and a
singular solution of the Liouville problem in the plane.
