Solid partitions are generalizations of plane partitions. MacMahon conjectured the generating function for the number of solid partitions was f(z) = 1/((1 - z)(1 - z^2)^3 (1 - z^3)^6 (1 - z^4)^10 ...), but this was subsequently shown to disagree at n = 6 . Knuth extended the tabulation of values, but was unable to find a correct generating function. The first few values are 1, 4, 10, 26, 59, 140, ... (OEIS A000293).
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