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).
1, 9, 72, 504, 3024, 15120, 60480, 181440, 362880, 362880, 32659200, 2906668800, 255786854400, 22253456332800, 1913797244620800, 162672765792768000, 13664512326592512000, 1134154523107178496000, 93000670894788636672000, 7533054342477879570432000
Offset: 0
Examples
a(3) = (10-3)*(10-2)*(10-1) = 7*8*9 = 504.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..400
Programs
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Maple
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 # second Maple program: a:= proc(n) option remember; `if`(n=0, 1, (10^length(n)-n)*a(n-1)) end: seq(a(n), n=0..30); # Alois P. Heinz, Sep 22 2015
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PARI
a(n) = prod(i=1, n, 10^(1+logint(i, 10))-i); \\ Jinyuan Wang, Aug 09 2025
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Python
from functools import cache def a(n): return 1 if n == 0 else (10**len(str(n))-n)*a(n-1) print([a(n) for n in range(21)]) # Michael S. Branicky, Aug 13 2025
Formula
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
Extensions
More terms from Emeric Deutsch, Jul 31 2005
a(0)=1 prepended by Alois P. Heinz, Aug 13 2025
Comments