A243757 - OEIS

%I #27 Sep 04 2021 03:54:37

%S 1,1,1,1,1,5,5,5,5,5,25,25,25,25,25,125,125,125,125,125,625,625,625,

%T 625,625,15625,15625,15625,15625,15625,78125,78125,78125,78125,78125,

%U 390625,390625,390625,390625,390625,1953125,1953125,1953125,1953125,1953125,9765625

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

%C This is the generalized factorial for A060904.

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

%C 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

%H Reinhard Zumkeller, <a href="/A243757/b243757.txt">Table of n, a(n) for n = 0..1000</a>

%H Tyler Ball, Tom Edgar, and Daniel Juda, <a href="http://dx.doi.org/10.4169/math.mag.87.2.135">Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem</a>, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.

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

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

%t Table[Product[5^IntegerExponent[k, 5], {k, 1, n}], {n, 0, 20}] (* _G. C. Greubel_, Dec 24 2016 *)

%o (Sage)

%o S=[0]+[5^valuation(i, 5) for i in [1..100]]

%o [prod(S[1:i+1]) for i in [0..99]]

%o (Haskell)

%o a243757 n = a243757_list !! n

%o a243757_list = scanl (*) 1 a060904_list

%o -- _Reinhard Zumkeller_, Feb 04 2015

%o (PARI) a(n) = prod(k=1,n, 5^valuation(k,5)); \\ _G. C. Greubel_, Dec 24 2016

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

%K nonn

%O 0,6

%A _Tom Edgar_, Jun 10 2014