Euler's Pentagonal Numbers Theorem/Corollary 2/Historical Note

Historical Note on Number of Partitions of Integer equals Sum of Sequence of Number of Partitions of Integers indexed by Generalized Pentagonal Numbers
had noticed, but had not formally proved, the result Generalized Pentagonal Numbers form Exponents of Infinite Product of $1 - x^n$.

However, he was so convinced of its truth that he used it to prove this and other results.