%I
%S 1,1,2,10,465,190131,848597563,43025433375905,26004966055138634525,
%T 194173310204064149748222455,18434259996904142171888712495703426,
%U 22778257480946919793779826285286813732062310,373444566958856976964193391832469245535883039838631492
%N Number of factorizations of m^n into n factors, where m is a product of exactly n distinct primes and each factor is a product of n primes (counted with multiplicity).
%C Also number of ways to partition the multiset consisting of n copies each of 1, 2, ..., n into n multisets of size n.
%F a(n) = A257462(n,n) = A257463(n,n).
%e a(3) = 10: (2*3*5)^3 = 2700 = 30*30*30 = 45*30*20 = 50*27*20 = 50*30*18 = 50*45*12 = 75*20*18 = 75*30*12 = 75*45*8 = 125*18*12 = 125*27*8.
%Y Main diagonal of A257462 and of A257463.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Apr 21 2020
%E More terms from _Andrew Howroyd_, Apr 21 2020
