A322488 Number of factorizations of the n-th power of the product of the first n primes.

1, 1, 9, 686, 911838, 27119992809, 23970534519938280, 790361842548583118561351, 1186709456459520739315771458325336, 96786580459441954551347685958203256606168610, 502265575410823018475962732653887865889973989497971475955

Offset

0,3

Comments

Also number of n-partite partitions of {n}^n into n-tuples. a(2) = 9: [(2,2)], [(2,1),(0,1)], [(2,0),(0,2)], [(2,0),(0,1),(0,1)], [(1,2),(1,0)], [(1,1),(1,1)], [(1,1),(1,0),(0,1)], [(1,0),(1,0),(0,2)], [(1,0),(1,0),(0,1),(0,1)].

Also number of partitions of the multiset with n copies each of 1,2,...,n. a(2) = 9: 1122, 11|22, 12|12, 1|122, 112|2, 11|2|2, 1|1|22, 1|12|2, 1|1|2|2.

Links

Table of n, a(n) for n=0..10.

Formula

a(n) = A001055(A181555(n)) = A001055(A002110(n)^n).

Example

a(2) = 9: (2*3)^2 = A002110(2)^2 = 36 has 9 factorizations: 36, 3*12, 4*9, 3*3*4, 2*18, 6*6, 2*3*6, 2*2*9, 2*2*3*3.

Crossrefs

Main diagonal of A219727.

Cf. A000040, A000110, A001055, A002110, A181555.

Sequence in context: A372184 A053973 A059492 * A109061 A332169 A282181

Adjacent sequences: A322485 A322486 A322487 * A322489 A322490 A322491

Keyword

nonn

Author

Alois P. Heinz, Dec 11 2018

Extensions

a(10) from Andrew Howroyd, Dec 11 2018

Status

approved