This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309415 #15 Jul 31 2019 20:40:42
%S A309415 1,1,1,1,2,6,6,12,60,360,1260,10080,15120,25200,1247400,32432400,
%T A309415 12612600,6810804000,7264857600,185253868800,1005663859200,
%U A309415 1117404288000,4839757322400,93504111468768000,37401644587507200,160787493266400000,13023786954578400000
%N A309415 Number of different numbers that are formed by permuting digits of n!.
%C A309415 a(0) = 1 because 0! = 1 has one permutation (1).
%C A309415 a(4) = 2 because 4! = 24 has two permutations (24, 42).
%C A309415 a(5) = 6 because 5! = 120 has 6 permutations (012, 021, 102, 120, 201, 210).
%H A309415 Alois P. Heinz, <a href="/A309415/b309415.txt">Table of n, a(n) for n = 0..460</a>
%p A309415 a:= n-> (l-> combinat[multinomial](add(i, i=l), l[])
%p A309415 )([coeffs(add(x^i, i=convert(n!, base, 10)))]):
%p A309415 seq(a(n), n=0..30); # _Alois P. Heinz_, Jul 30 2019
%t A309415 a[n_] := Block[{w = IntegerDigits[n!]}, Length[w]! / Times @@ ((Last /@ Tally[w])!)]; Array[a, 26, 0] (* _Giovanni Resta_, Jul 30 2019 *)
%o A309415 (Haskell)
%o A309415 import Data.List (permutations, nub)
%o A309415 factorial n = product [1..n]
%o A309415 a309415 n = length $ nub $ permutations $ show $ factorial n
%o A309415 map a309415 [0..]
%Y A309415 Cf. A000142, A047726.
%K A309415 nonn,base
%O A309415 0,5
%A A309415 _Hauke Löffler_, Jul 30 2019
%E A309415 More terms from _Giovanni Resta_, Jul 30 2019