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We show that the numberof partitions with  m  even parts and largest hook length  n  is strongly unimodal with modefor. We establish this result by induction, using a 5-term recurrence due to Lin, Xiong and Yan, and two 4-term recurrences obtained by Zeilberger's algorithm. The sequenceis not log-concave. Using Möbius transformation and the method of interlacing zeros, we obtain that every zero of every generating polynomiallies on the left half part of the circle. Moreover, as an application of Wang and Zhang's characterization of root geometry of polynomial sequences that satisfy a recurrence, we confirm that the zeros are densely distributed on the half circle.

A unimodal sequence with mode at a quarter length