me braindead as usual... The relation was
P(x^2)^8 + 16*x*P(x^2)^16*P(x)^8 = P(x)^16
[...something wrong...]
Here we go (ND='number of partitions into distinct parts'): ND of n using 16 different fonts [P(x)^16] equals ND of n into even parts using 8 fonts [P(x^2)^8], plus 16 times ND of n-1 [16*x* ] into even parts using 16 fonts [ *P(x^2)^16* ] and into arbitrary parts using 8 fonts [ *P(x)^8]. @ Dirk: 'fonts' := 'kinds of parts' (really: kinds of letters) @ RWG: I now see your odd 'odd' comes from this: P(x)/P(x^2) = prod(k=0, 00, 1 + x^(2k+1) ) =: O(x), so P(x^2)^16*P(x)^8 == P(x^2)^24 * O(x^8) So you secretely write the relation as
P(x^2)^8 + 16*x*P(x^2)^24*O(x^8) = P(x)^16
and you interpretation is correct as given: The number of partitions of n into distinct integers using 16 different fonts equals the number of partitions of n into distinct even parts using 8 fonts, plus 16 times the number of partitions of n-1 into distinct even parts using 24 fonts and distinct odd parts using 8 fonts.
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