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

1, 1, 6, 138, 14049, 6851919

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..5.

John Tyler Rascoe, Python program.

Formula

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

Example

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.

Prog

(Python) # see Links

Crossrefs

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

Sequence in context: A307353 A366227 A155558 * A053467 A288557 A288565

Adjacent sequences: A385370 A385371 A385372 * A385374 A385375 A385376

Keyword

nonn,more

Author

John Tyler Rascoe, Jun 27 2025

Status

approved