login
a(n) = Product_{i=1..n} A234959(i).
3

%I #20 Dec 25 2016 02:28:32

%S 1,1,1,1,1,1,6,6,6,6,6,6,36,36,36,36,36,36,216,216,216,216,216,216,

%T 1296,1296,1296,1296,1296,1296,7776,7776,7776,7776,7776,7776,279936,

%U 279936,279936,279936,279936,279936,1679616,1679616,1679616,1679616,1679616,1679616,10077696

%N a(n) = Product_{i=1..n} A234959(i).

%C This is the generalized factorial for A234959.

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

%H Reinhard Zumkeller, <a href="/A243758/b243758.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} A234959(i).

%F a(n) = 6^(A054895(n)).

%t Table[Product[6^IntegerExponent[k, 6], {k, 1, n}], {n, 0, 20}] (* _G. C. Greubel_, Dec 24 2016 *)

%o (Sage)

%o S=[0]+[6^valuation(i,6) for i in [1..100]]

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

%o (Haskell)

%o a243758 n = a243758_list !! n

%o a243758_list = scanl (*) 1 a234959_list

%o -- _Reinhard Zumkeller_, Feb 09 2015

%o (PARI) valp(n,p)=my(s); while(n\=p, s+=n); s

%o a(n)=6^valp(n,6) \\ _Charles R Greathouse IV_, Oct 03 2016

%Y Cf. A060828, A060818, A234959, A242954, A243757.

%K nonn,easy

%O 0,7

%A _Tom Edgar_, Jun 10 2014