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A055098 Number of distinct anagrams of digits of n without leading zeros.

%I A055098 #22 Oct 11 2022 14:11:33
%S A055098 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,1,2,1,2,2,2,2,2,2,2,1,2,2,1,2,
%T A055098 2,2,2,2,2,1,2,2,2,1,2,2,2,2,2,1,2,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,2,
%U A055098 2,1,2,2,2,2,2,2,1,2,2,1,2,2,2,2,2,2,2,1,2,1,2,2,2,2,2,2,2,2,1,1,2,4
%N A055098 Number of distinct anagrams of digits of n without leading zeros.
%H A055098 Reinhard Zumkeller, <a href="/A055098/b055098.txt">Table of n, a(n) for n = 1..10000</a>
%F A055098 a(n) = O(n/(log n)^(9/2)). - _Charles R Greathouse IV_, Aug 24 2022
%e A055098 a(101)=2 since the digits of 101 can be ordered 101 or 110 (but not 011).
%t A055098 a[n_] := Length[ DeleteCases[ Permutations[ IntegerDigits[n]], {0 .., __}]]; Table[a[n], {n, 1, 102}] (* _Jean-François Alcover_, Nov 30 2011 *)
%o A055098 (Haskell)
%o A055098 import Data.List (permutations, nub)
%o A055098 a055098 n = length $ nub $ filter ((> '0') . head) $ permutations $ show n
%o A055098 -- _Reinhard Zumkeller_, Aug 14 2011
%o A055098 (PARI) a(n)={my(v=digits(n), f=vector(10), n=#v); for(i=1, #v, f[1+v[i]]++); (1 - f[1]/n) * n! / prod(i=1, #f, f[i]!)} \\ _Andrew Howroyd_, Jan 27 2020
%o A055098 (Python)
%o A055098 from math import factorial, prod
%o A055098 def a(n):
%o A055098     s = str(n); d, c = len(s), [s.count(str(i)) for i in range(10)]
%o A055098     return (d-c[0])*factorial(d-1)//prod(map(factorial, c))
%o A055098 print([a(n) for n in range(1, 50)]) # _Michael S. Branicky_, Aug 24 2022
%Y A055098 Cf. A046810, A047726.
%K A055098 base,easy,nice,nonn
%O A055098 1,12
%A A055098 _Henry Bottomley_, Apr 19 2000