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

Author

Amarnath Murthy, Jul 29 2005

Keywords

• nonn
• base
• easy

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

Crossrefs

Cf. A089186, A109631, A110394, A110395.

Programs

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

PARI

a(n) = prod(i=1, n, 10^(1+logint(i, 10))-i); \\ Jinyuan Wang, Aug 09 2025

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