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A110396 10's complement factorial of n: a(n) = (10's complement of n)*(10's complement of n-1)*...*(10's complement of 2)*(10's complement of 1).

%I A110396 #33 Aug 13 2025 19:16:42
%S A110396 1,9,72,504,3024,15120,60480,181440,362880,362880,32659200,2906668800,
%T A110396 255786854400,22253456332800,1913797244620800,162672765792768000,
%U A110396 13664512326592512000,1134154523107178496000,93000670894788636672000,7533054342477879570432000
%N A110396 10's complement factorial of n: a(n) = (10's complement of n)*(10's complement of n-1)*...*(10's complement of 2)*(10's complement of 1).
%H A110396 Alois P. Heinz, <a href="/A110396/b110396.txt">Table of n, a(n) for n = 0..400</a>
%F A110396 a(n) = Product_{i=1..n} c(i), where c(i) = A089186(i) is the difference between i and the next power of 10 (for example, c(13) = 100 - 13 = 87; c(100) = 1000 - 100 = 900). - _Emeric Deutsch_, Jul 31 2005
%e A110396 a(3) = (10-3)*(10-2)*(10-1) = 7*8*9 = 504.
%p A110396 s:=proc(m) nops(convert(m,base,10)) end: for q from 1 to 120 do c[q]:=10^s(q)-q od: a:=n->product(c[i],i=1..n): seq(a(n),n=0..20); # _Emeric Deutsch_, Jul 31 2005
%p A110396 # second Maple program:
%p A110396 a:= proc(n) option remember; `if`(n=0, 1,
%p A110396        (10^length(n)-n)*a(n-1))
%p A110396     end:
%p A110396 seq(a(n), n=0..30);  # _Alois P. Heinz_, Sep 22 2015
%o A110396 (PARI) a(n) = prod(i=1, n, 10^(1+logint(i, 10))-i); \\ _Jinyuan Wang_, Aug 09 2025
%o A110396 (Python)
%o A110396 from functools import cache
%o A110396 def a(n): return 1 if n == 0 else (10**len(str(n))-n)*a(n-1)
%o A110396 print([a(n) for n in range(21)]) # _Michael S. Branicky_, Aug 13 2025
%Y A110396 Cf. A089186, A109631, A110394, A110395.
%K A110396 nonn,base,easy
%O A110396 0,2
%A A110396 _Amarnath Murthy_, Jul 29 2005
%E A110396 More terms from _Emeric Deutsch_, Jul 31 2005
%E A110396 a(0)=1 prepended by _Alois P. Heinz_, Aug 13 2025