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

0,3

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

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.

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 *)

Prog

(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

Crossrefs

Cf. A000142, A000351, A002266, A047201.

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

Sequence in context: A013068 A326780 A365976 * A375812 A375808 A258325

Adjacent sequences: A356855 A356856 A356857 * A356859 A356860 A356861

Keyword

nonn

Author

Stefano Spezia, Sep 01 2022

Status

approved