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%I #19 Aug 16 2021 19:56:35
%S 1,1,9,686,911838,27119992809,23970534519938280,
%T 790361842548583118561351,1186709456459520739315771458325336,
%U 96786580459441954551347685958203256606168610,502265575410823018475962732653887865889973989497971475955
%N Number of factorizations of the n-th power of the product of the first n primes.
%C 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)].
%C 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.
%F a(n) = A001055(A181555(n)) = A001055(A002110(n)^n).
%e 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.
%Y Main diagonal of A219727.
%Y Cf. A000040, A000110, A001055, A002110, A181555.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Dec 11 2018
%E a(10) from _Andrew Howroyd_, Dec 11 2018
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