Solid partitions are generalizations of plane partitions. MacMahon (1960) conjectured the generating function
for the number of solid partitions was

but this was subsequently shown to disagree at (Atkin et al. 1967). Knuth (1970) 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).

Atkin, A. O. L.; Bratley, P.; Macdonald, I. G.; and McKay, J. K. S. "Some Computations for -Dimensional Partitions." Proc. Cambridge Philos. Soc.63,
1097-1100, 1967.Knuth, D. E. "A Note on Solid Partitions."
Math. Comput.24, 955-961, 1970.MacMahon, P. A. "Memoir
on the Theory of the Partitions of Numbers. VI: Partitions in Two-Dimensional Space,
to which is Added an Adumbration of the Theory of Partitions in Three-Dimensional
Space." Phil. Trans. Roy. Soc. London Ser. A211, 345-373, 1912.MacMahon,
P. A. Combinatory
Analysis, Vol. 2. New York: Chelsea, pp. 75-176, 1960.Sloane,
N. J. A. Sequence A000293/M3392
in "The On-Line Encyclopedia of Integer Sequences."