A004154 a(n) = n! with trailing zeros omitted.

1, 1, 2, 6, 24, 12, 72, 504, 4032, 36288, 36288, 399168, 4790016, 62270208, 871782912, 1307674368, 20922789888, 355687428096, 6402373705728, 121645100408832, 243290200817664, 5109094217170944, 112400072777760768, 2585201673888497664, 62044840173323943936

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..250
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000142, A004151, A008904 (mod 10).

Programs

Haskell

a004154 = a004151 . a000142
a004154_list = scanl (\u v -> a004151 $ u * v) 1 [1..]
-- Reinhard Zumkeller, Nov 24 2012

Magma

[Factorial(n)/10^Valuation(Factorial(n), 5): n in [0..30]]; // Vincenzo Librandi, Oct 16 2014

Maple

a:= n-> (f-> f/10^padic[ordp](f,10))(n!):
seq(a(n), n=0..29);  # Alois P. Heinz, Dec 29 2021

Mathematica

Array[#!//.x_/;x~Mod~5==0:>x/10&,22]  (* Giorgos Kalogeropoulos, Aug 17 2020 *)
Join[{1,1,2,6,24},Table[FromDigits[Flatten[Most[Split[IntegerDigits[n!]]]]],{n,5,30}]] (* or *) Table[n!/10^IntegerExponent[n!,10],{n,0,30}] (* Harvey P. Dale, Feb 13 2024 *)

PARI

a(n)=n!/10^valuation(n!,5) \\ M. F. Hasler, Oct 16 2014

Python

from sympy import factorial
from sympy.ntheory.factor_ import digits
def A004154(n): return factorial(n)//10**(n-sum(digits(n,5)[1:])>>2) # Chai Wah Wu, Oct 18 2024

Python

from itertools import count, islice
def agen(): # generator of terms
    f = 1
    for n in count(1):
        yield f
        while n%10 == 0: n //= 10
        f *= n
        while f%10 == 0: f //= 10
print(list(islice(agen(), 25))) # Michael S. Branicky, Apr 11 2025

Formula

a(n) = A000142(n) / 10^A027868(n). - Reinhard Zumkeller, Nov 24 2012

a(n+1) = A004151((n+1)*a(n)). - Reinhard Zumkeller, Nov 24 2012, corrected by M. F. Hasler, Oct 16 2014

a(n) = A004151(A000142(n)) = A000142(n)/A011557(A112765(n)), or A122840 instead of A112765. - M. F. Hasler, Oct 16 2014