A356858 a(n) is the product of the first n numbers not divisible by 5.

1, 1, 2, 6, 24, 144, 1008, 8064, 72576, 798336, 9580032, 124540416, 1743565824, 27897053184, 474249904128, 8536498274304, 162193467211776, 3406062811447296, 74933381851840512, 1723467782592331776, 41363226782215962624, 1075443896337615028224, 29036985201115605762048

Offset: 0

Author

Stefano Spezia, Sep 01 2022

Keywords

• nonn

Comments

Unlike the factorial number n!, a(n) does not have trailing zeros.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..434

Crossrefs

Cf. A000142, A000351, A002266, A047201.

Cf. A356859 (number of zero digits), A356860 (number of digits), A356861 (number of nonzero digits).

Programs

Mathematica

Table[Product[Floor[(5k-1)/4], {k,n}], {n,0,22}] (* or *)
Join[{1}, Table[Floor[(5n-1)/4]!/(Floor[Floor[(5n-1)/4]/5]!*5^Floor[Floor[(5n-1)/4]/5]), {n,22}]]
Join[{1},FoldList[Times,Table[If[Mod[n,5]==0,Nothing,n],{n,30}]]] (* Harvey P. Dale, Nov 03 2024 *)

Python

from math import prod
def a(n): return prod((5*k-1)//4 for k in range(1, n+1))
print([a(n) for n in range(23)]) # Michael S. Branicky, Sep 01 2022

Formula

a(n) = Product_{k=1..n} A047201(k).

a(n) = A047201(n)!/(floor(A047201(n)/5)!*5^floor(A047201(n)/5)) for n > 0.