A379277 -id:A379277 - cp's OEIS frontend

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A385373 Number of solid partitions with multiplicities (1, ..., n).

Original entry on oeis.org

1, 1, 6, 138, 14049, 6851919

Offset: 0

John Tyler Rascoe, Jun 27 2025

A solid partition with d distinct parts (p_1^(k_1) > p_2^(k_2) > ... > p_d^(k_d)) has the multiset of multiplicities (k_1, k_2, ..., k_d).

Alternatively, a(n) is the number of chains of plane partitions ordered by inclusion, comprised of n consecutive triangular numbers starting with 1.

			For n = 2 a solid partition having multiplicities (1,2) has two distinct parts (a,b^2) with a < b, and there are 6 ways to arrange these parts.

John Tyler Rascoe, Python program.

Cf. A000217, A000219, A000293, A164894, A379277.

Python
```
# see Links
```

a(n) = A379277(A164894(n)) for n > 0.

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