How many different ways could I factor $2^{2n}$ so that each factor is a even power of $2$? So for example if I have $2^{12}$ and I want to write it as 3 factors of even powers of $2$ I could do $2^{2} \cdot 2^4 \cdot 2^6$.
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1Hint: How many ways can you partition a natural number as a sum of natural numbers. – Jack LeGrüß Oct 09 '20 at 17:10
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2Surely $2^0=1$ is not an even power of two, right? – Parcly Taxel Oct 09 '20 at 17:16