A309415 Number of different numbers that are formed by permuting digits of n!.

1, 1, 1, 1, 2, 6, 6, 12, 60, 360, 1260, 10080, 15120, 25200, 1247400, 32432400, 12612600, 6810804000, 7264857600, 185253868800, 1005663859200, 1117404288000, 4839757322400, 93504111468768000, 37401644587507200, 160787493266400000, 13023786954578400000

Offset: 0

Author

Hauke Löffler, Jul 30 2019

Keywords

• nonn
• base

Comments

a(0) = 1 because 0! = 1 has one permutation (1).

a(4) = 2 because 4! = 24 has two permutations (24, 42).

a(5) = 6 because 5! = 120 has 6 permutations (012, 021, 102, 120, 201, 210).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..460

Crossrefs

Cf. A000142, A047726.

Programs

Haskell

import Data.List (permutations, nub)
factorial n = product [1..n]
a309415 n = length $ nub $ permutations $ show $ factorial n
map a309415 [0..]

Maple

a:= n-> (l-> combinat[multinomial](add(i, i=l), l[])
      )([coeffs(add(x^i, i=convert(n!, base, 10)))]):
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 30 2019

Mathematica

a[n_] := Block[{w = IntegerDigits[n!]}, Length[w]! / Times @@ ((Last /@ Tally[w])!)]; Array[a, 26, 0] (* Giovanni Resta, Jul 30 2019 *)

Extensions

More terms from Giovanni Resta, Jul 30 2019