OEIS A00291: Bipartite partitions

In this episode of The Deep Dive we explore A00291, the bipartite partitions sequence. We unpack its multiple lives: counting bipartitions of N white objects with two black ones; counting factorizations of P^N Q^2 with distinct primes; and relating to multiset partitions of a 2-element multiset. We also discuss connections to other fundamental OEIS sequences (like A000070 and A00097), the asymptotic growth formula, and the notable contributors—Sloan, Chima, Gupta, Knuth—whose work helped reveal the underlying structure. It’s a vivid example of how a simple counting problem can bridge combinatorics and number theory, inviting you to explore the rich web of links in the OEIS.

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