A207646 Product_{k=1..n} floor(2*n/k - 1).

1, 1, 3, 10, 21, 72, 330, 468, 2520, 8160, 20520, 60480, 318780, 504000, 2426112, 10523520, 21092400, 53222400, 452390400, 506373120, 3226728960, 11604902400, 21299241600, 76640256000, 431500608000, 844958822400, 3197988864000, 10492449177600, 38109367296000

Offset: 0

Author

Paul D. Hanna, Feb 20 2012

Keywords

• nonn

Comments

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

Examples

			Illustration of the initial terms:
a(1) = [2/1-1] = 1;
a(2) = [4/1-1]*[4/2-1] = 3;
a(3) = [6/1-1]*[6/2-1]*[6/3-1] = 10;
a(4) = [8/1-1]*[8/2-1]*[8/3-1]*[8/4-1] = 21;
a(5) = [10/1-1]*[10/2-1]*[10/3-1]*[10/4-1]*[10/5-1] = 72; ...
where [x] = floor(x).
		

Links

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

Crossrefs

Cf. A207645, A207647, A207643, A207644.

Programs

Mathematica

Table[Product[Floor[(2n)/k-1],{k,n}],{n,0,30}] (* Harvey P. Dale, Aug 27 2017 *)

PARI

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

PARI

a(n)=n*=2;prod(k=1,n/3,n\k-1) \\ Charles R Greathouse IV, Feb 20 2012

Formula

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