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%I #29 Sep 08 2022 08:45:06
%S 9,81,648,4536,27216,136080,544320,1632960,3265920,3265920
%N Number of n-digit positive integers with all digits distinct.
%C For any base b the number of distinct-digit numbers is finite. For base 10, the maximal distinct-digit number is 9876543210; for any larger number at least two digits coincide. The number of distinct-digit primes is also finite, see A073532.
%C If "positive" is replaced by "nonnegative" we get the sequence 10, 81, 648, 4536, 27216, 136080, 544320, 1632960, 3265920, 3265920.
%C Alternatively, if 0 is considered to have 0 digits, one could prefix a(0) = 1. This would be compatible with the given formula and 9/10 rounded to the nearest integer. - _M. F. Hasler_, Dec 10 2018
%C a(10) is the final term because no number having more than 10 digits can have all digits distinct. - _Jon E. Schoenfield_, May 17 2021
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Digit.html">Digit</a>
%F a(n) = 9*9!/(10-n)!.
%e a(3) = 648 because there are 648 three-digit integers with distinct digits.
%p seq(9*factorial(9)/(factorial(10-n)),n=1..10); # _Muniru A Asiru_, Dec 11 2018
%t Table[9*9!/(10-n)!, {n, 10}]
%o (PARI) apply( A073531(n)=if(n<11,9*9!\/(10-n)!), [1..13]) \\ or: 9*binomial(9,10-n)*(n-1)! without need for if(). - _M. F. Hasler_, Dec 10 2018
%o (GAP) List([1..10],n->9*Factorial(9)/(Factorial(10-n))); # _Muniru A Asiru_, Dec 11 2018
%o (Magma) [9*Factorial(9)/Factorial(10-n): n in [1..10]]; // _Vincenzo Librandi_, Dec 13 2018
%Y Cf. A073532.
%Y Cf. A010784 for the list of these integers.
%K nonn,base,fini,full
%O 1,1
%A _Zak Seidov_, Aug 29 2002
%E Keywords fini, full added by _Jon E. Schoenfield_, May 17 2021
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