A325617 Multinomial coefficient of the prime signature of n!.

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!.

Links

Table of n, a(n) for n=0..22.

Wikipedia, Multinomial theorem

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}]

Crossrefs

Cf. A000142, A008480, A011371, A022559, A076934, A108731, A115627, A318762, A325272, A325273, A325508, A325543, A325544, A325609.

Sequence in context: A337038 A058006 A153229 * A013329 A364393 A324311

Adjacent sequences: A325614 A325615 A325616 * A325618 A325619 A325620

Keyword

nonn

Author

Gus Wiseman, May 12 2019

Status

approved