We explore the counting problem behind A00348: take the set {1^2, 2^2, ..., (2n)^2 } and pair its elements into disjoint pairs so that the sum of the two numbers in each pair is prime. Interpreting this as a graph of allowed pairings, the sequence counts the number of perfect matchings. We'll cover the basic definition, walk through small cases, discuss computational approaches for larger instances, and touch on connections to graph theory and the distribution of primes.

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