Problem concerned with A018819

[Vladeta Jovovic]

Seqfans,


Let p be a partition of n.

Define Perm(p)  to be the number of permutations on p (if we consider p as a multiset) or equivalently the number of compositions generated by p.

Then, it seems that 

number of partitions p of n such that Perm(p) is odd  =  number of partitions of n into powers of 2  =  A018819(n) .

Is there a (simple bijective) proof of this conjecture?


Best regards,

Vladeta Jovovic
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