Abstract
Using quasimodular forms with respect to Γ0(4) we find exact relations between the M2-rank for partitions without repeated odd parts and three residual cranks. From these identities we are able to deduce various congruences mod 3 and 5 between the rank and crank moments. In turn, these congruences give congruences for M2spt (n), the number of occurrences of smallest parts in the partitions of n with smallest part even and without repeated odd parts, and for the higher-order analog M2spt2 (n).
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