login
A243757
a(n) = Product_{i=1..n} A060904(i).
4
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
0,6
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
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.
FORMULA
a(n) = Product_{i=1..n} A060904(i).
a(n) = 5^(A027868(n)).
MATHEMATICA
Table[Product[5^IntegerExponent[k, 5], {k, 1, n}], {n, 0, 20}] (* G. C. Greubel, Dec 24 2016 *)
PROG
(Sage)
S=[0]+[5^valuation(i, 5) for i in [1..100]]
[prod(S[1:i+1]) for i in [0..99]]
(Haskell)
a243757 n = a243757_list !! n
a243757_list = scanl (*) 1 a060904_list
-- Reinhard Zumkeller, Feb 04 2015
(PARI) a(n) = prod(k=1, n, 5^valuation(k, 5)); \\ G. C. Greubel, Dec 24 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Tom Edgar, Jun 10 2014
STATUS
approved