The form of electron correlations in a partially filled degenerate Landau level (LL) is related to the behavior of the anharmonic part of the interaction pseudopotential. Unlike in the lowest LL, the pseudopotential in the first excited LL is harmonic at short range. As a result, the incompressible states in this LL have different correlations, occur at different filling factors nu, and cannot be described by a composite fermion model. The series of Laughlin-correlated states of electron pairs is proposed at nu=2+2/(q_2+2) with integer q_2. It includes Moore-Read nu=5/2 state and the nu=7/3 state. Despite coincidence of the values of nu, the latter state has different correlations than Laughlin state of single electrons at nu=1/3 and, in finite systems, occurs at a different LL degeneracy (flux).