A243757 a(n) = Product_{i=1..n} A060904(i).

1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 25, 25, 25, 25, 25, 125, 125, 125, 125, 125, 625, 625, 625, 625, 625, 15625, 15625, 15625, 15625, 15625, 78125, 78125, 78125, 78125, 78125, 390625, 390625, 390625, 390625, 390625, 1953125, 1953125, 1953125, 1953125, 1953125, 9765625

Offset: 0

Author

Tom Edgar, Jun 10 2014

Keywords

• nonn

Comments

This is the generalized factorial for A060904.

a(0) = 1 as it represents the empty product.

a(n) is the largest power of 5 that divides n!, or the order of a 5-Sylow subgroup of the symmetric group of degree n. - David Radcliffe, Sep 03 2021

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.

Crossrefs

Cf. A027868, A060818, A060828, A060904, A242954.

Programs

Haskell

a243757 n = a243757_list !! n
a243757_list = scanl (*) 1 a060904_list
-- Reinhard Zumkeller, Feb 04 2015

Mathematica

Table[Product[5^IntegerExponent[k, 5], {k, 1, n}], {n, 0, 20}] (* G. C. Greubel, Dec 24 2016 *)

PARI

a(n) = prod(k=1,n, 5^valuation(k,5)); \\ G. C. Greubel, Dec 24 2016

Sage

S=[0]+[5^valuation(i, 5) for i in [1..100]]
[prod(S[1:i+1]) for i in [0..99]]

Formula

a(n) = Product_{i=1..n} A060904(i).

a(n) = 5^(A027868(n)).