A207647 a(n) = Product_{k=1..n} floor((2*n+1)/k - 1).

1, 2, 4, 12, 48, 80, 360, 1344, 2688, 8640, 51840, 63360, 443520, 1198080, 2515968, 10886400, 48384000, 87736320, 465315840, 1134673920, 3309465600, 11887948800, 71530905600, 78343372800, 528817766400, 1839366144000, 3260694528000, 15837659136000, 82169502105600

Offset: 0

Author

Paul D. Hanna, Feb 20 2012

Keywords

• nonn

Comments

Forms the right border of odd-indexed rows in irregular triangle A207645.

Examples

			Illustration of the initial terms:
a(1) = [3/1-1] = 2;
a(2) = [5/1-1]*[5/2-1] = 4;
a(3) = [7/1-1]*[7/2-1]*[7/3-1] = 12;
a(4) = [9/1-1]*[9/2-1]*[9/3-1]*[9/4-1] = 48;
a(5) = [11/1-1]*[11/2-1]*[11/3-1]*[11/4-1]*[11/5-1] = 80; ...
where [x] = floor(x).
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A207645, A207646, A207643, A207644.

Programs

Mathematica

Table[Product[Floor[(2n+1)/k-1],{k,n}],{n,0,30}] (* Harvey P. Dale, Jun 01 2019 *)

PARI

{a(n)=prod(k=1,n,floor((2*n+1)/k-1))}
for(n=0,50,print1(a(n),", "))

Formula

a(n) = A207645(2*n+1, n).