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A325617
Multinomial coefficient of the prime signature of n!.
28
1, 1, 1, 2, 4, 20, 105, 840, 3960, 51480, 675675, 10810800, 139675536, 2793510720, 58663725120, 1799020903680, 26985313555200, 782574093100800, 25992639520848000, 857757104187984000, 30021498646579440000, 1563341744336692320000, 64179292662243158400000
OFFSET
0,4
COMMENTS
Number of permutations of the multiset of prime factors of n!.
FORMULA
a(n) = A318762(A181819(n!)).
EXAMPLE
The a(5) = 20 permutations of {2,2,2,3,5}:
(22235) (32225) (52223)
(22253) (32252) (52232)
(22325) (32522) (52322)
(22352) (35222) (53222)
(22523)
(22532)
(23225)
(23252)
(23522)
(25223)
(25232)
(25322)
MATHEMATICA
Table[Multinomial@@Last/@FactorInteger[n!], {n, 0, 15}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 12 2019
STATUS
approved