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

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

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

Example

a(3) = (10-3)*(10-2)*(10-1) = 7*8*9 = 504.

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
# Alternative:
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

Prog

(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

Crossrefs

Cf. A089186, A109631, A110394, A110395.

Sequence in context: A288351 A319892 A319873 * A162755 A396209 A378483

Adjacent sequences: A110393 A110394 A110395 * A110397 A110398 A110399

Keyword

nonn,base,easy

Author

Amarnath Murthy, Jul 29 2005

Extensions

More terms from Emeric Deutsch, Jul 31 2005

a(0)=1 prepended by Alois P. Heinz, Aug 13 2025

Status

approved