A325617 - OEIS

%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