A243758 a(n) = Product_{i=1..n} A234959(i).

1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 36, 36, 36, 36, 36, 36, 216, 216, 216, 216, 216, 216, 1296, 1296, 1296, 1296, 1296, 1296, 7776, 7776, 7776, 7776, 7776, 7776, 279936, 279936, 279936, 279936, 279936, 279936, 1679616, 1679616, 1679616, 1679616, 1679616, 1679616, 10077696

Offset

0,7

Comments

This is the generalized factorial for A234959.

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

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.

Formula

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

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

Mathematica

Table[Product[6^IntegerExponent[k, 6], {k, 1, n}], {n, 0, 20}] (* G. C. Greubel, Dec 24 2016 *)

Prog

(Sage)
S=[0]+[6^valuation(i, 6) for i in [1..100]]
[prod(S[1:i+1]) for i in [0..99]]
(Haskell)
a243758 n = a243758_list !! n
a243758_list = scanl (*) 1 a234959_list
-- Reinhard Zumkeller, Feb 09 2015
(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
a(n)=6^valp(n, 6) \\ Charles R Greathouse IV, Oct 03 2016

Crossrefs

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

Sequence in context: A103337 A241155 A245399 * A318355 A318237 A201572

Adjacent sequences: A243755 A243756 A243757 * A243759 A243760 A243761

Keyword

nonn,easy

Author

Tom Edgar, Jun 10 2014

Status

approved