We demonstrate the successive appearance of the exciton, biexciton, and P band of the exciton-exciton scattering with increasing excitation power in the photoluminescence of indium selenide layered crystals. The strict energy and momentum conservation rules of the P band are used to reexamine the exciton binding energy. The new value $geq 20$ meV is markedly higher than the currently accepted 14 meV, being however well consistent with the robustness of excitons up to room temperature. A peak controlled by the Sommerfeld factor is found near the bandgap ($sim 1.36$ eV), which puts the question on the pure three-dimensional character of the exciton in InSe, which has been assumed up to now. Our findings are of paramount importance for the successful application of InSe in nanophotonics.
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