A333144 Irregular triangle where row n lists the product of the factorials of the exponentials of the partitions of n and the partitions are enumerated in canonical order.

1, 1, 1, 2, 1, 1, 6, 1, 1, 2, 2, 24, 1, 1, 1, 2, 2, 6, 120, 1, 1, 1, 2, 2, 1, 6, 6, 4, 24, 720, 1, 1, 1, 2, 1, 1, 6, 2, 2, 2, 24, 6, 12, 120, 5040, 1, 1, 1, 2, 1, 1, 6, 2, 1, 2, 2, 24, 2, 4, 2, 6, 120, 24, 12, 48, 720, 40320

Offset

0,4

Comments

By 'canonical order' we understand the graded reverse lexicographic order (the default order of Mathematica and SageMath).

Links

Table of n, a(n) for n=0..66.

Example

The irregular table starts:
[0] [1]
[1] [1]
[2] [1, 2]
[3] [1, 1, 6]
[4] [1, 1, 2, 2, 24]
[5] [1, 1, 1, 2, 2, 6, 120]
[6] [1, 1, 1, 2, 2, 1, 6, 6, 4, 24, 720]
[7] [1, 1, 1, 2, 1, 1, 6, 2, 2, 2, 24, 6, 12, 120, 5040]

Prog

(SageMath)
def A333144row(n):
    return [product(factorial(expo) for expo in partition.to_exp()) for partition in Partitions(n)]
for n in (0..9): print(A333144row(n))

Crossrefs

Row sums are A161779.

Cf. A069123.

Sequence in context: A216919 A152656 A096162 * A306297 A053383 A181538

Adjacent sequences: A333141 A333142 A333143 * A333145 A333146 A333147

Keyword

nonn,tabf

Author

Peter Luschny, Apr 10 2020

Status

approved