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

0,5

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

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 *)

Prog

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

Crossrefs

Cf. A000142, A047726.

Sequence in context: A140880 A065420 A119312 * A051398 A073131 A206490

Adjacent sequences: A309412 A309413 A309414 * A309416 A309417 A309418

Keyword

nonn,base

Author

Hauke Löffler, Jul 30 2019

Extensions

More terms from Giovanni Resta, Jul 30 2019

Status

approved