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%I #7 May 13 2019 01:10:42
%S 1,1,1,2,4,20,105,840,3960,51480,675675,10810800,139675536,2793510720,
%T 58663725120,1799020903680,26985313555200,782574093100800,
%U 25992639520848000,857757104187984000,30021498646579440000,1563341744336692320000,64179292662243158400000
%N Multinomial coefficient of the prime signature of n!.
%C Number of permutations of the multiset of prime factors of n!.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Multinomial_theorem">Multinomial theorem</a>
%F a(n) = A318762(A181819(n!)).
%e The a(5) = 20 permutations of {2,2,2,3,5}:
%e (22235) (32225) (52223)
%e (22253) (32252) (52232)
%e (22325) (32522) (52322)
%e (22352) (35222) (53222)
%e (22523)
%e (22532)
%e (23225)
%e (23252)
%e (23522)
%e (25223)
%e (25232)
%e (25322)
%t Table[Multinomial@@Last/@FactorInteger[n!],{n,0,15}]
%Y Cf. A000142, A008480, A011371, A022559, A076934, A108731, A115627, A318762, A325272, A325273, A325508, A325543, A325544, A325609.
%K nonn
%O 0,4
%A _Gus Wiseman_, May 12 2019
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