%I
%S 1,1,9,686,911838,27119992809,23970534519938280,
%T 790361842548583118561351,1186709456459520739315771458325336,
%U 96786580459441954551347685958203256606168610,502265575410823018475962732653887865889973989497971475955
%N Number of factorizations of the nth power of the product of the first n primes.
%C Also number of npartite partitions of {n}^n into ntuples. 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)].
%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. A002110.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Dec 11 2018
%E a(10) from _Andrew Howroyd_, Dec 11 2018
