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We consider solutions $u_p$ satisfying $p \\int_{\\Omega}\\abs{\\nabla u_p}^2\\to 16\\pi e\\quad\\hbox{as}p\\rightarrow+\\infty\\qquad (*)$ and we are interested in the shape and the asymptotic behavior as $p\\rightarrow+\\infty$. First we prove that (*) holds for least energy nodal solutions. Then we obtain some estimates and the asymptotic profile of this kind of solutions. 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