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A322488 Number of factorizations of the n-th power of the product of the first n primes. 1
1, 1, 9, 686, 911838, 27119992809, 23970534519938280, 790361842548583118561351, 1186709456459520739315771458325336, 96786580459441954551347685958203256606168610, 502265575410823018475962732653887865889973989497971475955 (list; graph; refs; listen; history; text; internal format)
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)].

LINKS

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

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. A002110.

Sequence in context: A287937 A053973 A059492 * A109061 A282181 A053515

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

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Last modified August 22 20:42 EDT 2019. Contains 326197 sequences. (Running on oeis4.)