A309415 - OEIS

%I #15 Jul 31 2019 20:40:42

%S 1,1,1,1,2,6,6,12,60,360,1260,10080,15120,25200,1247400,32432400,

%T 12612600,6810804000,7264857600,185253868800,1005663859200,

%U 1117404288000,4839757322400,93504111468768000,37401644587507200,160787493266400000,13023786954578400000

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

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

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

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

%H Alois P. Heinz, <a href="/A309415/b309415.txt">Table of n, a(n) for n = 0..460</a>

%p a:= n-> (l-> combinat[multinomial](add(i, i=l), l[])

%p       )([coeffs(add(x^i, i=convert(n!, base, 10)))]):

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Jul 30 2019

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

%o (Haskell)

%o import Data.List (permutations, nub)

%o factorial n = product [1..n]

%o a309415 n = length $ nub $ permutations $ show $ factorial n

%o map a309415 [0..]

%Y Cf. A000142, A047726.

%K nonn,base

%O 0,5

%A _Hauke Löffler_, Jul 30 2019

%E More terms from _Giovanni Resta_, Jul 30 2019