A061778 a(n) = Product_{j=0..floor(n/2)} binomial(n,j).

1, 2, 3, 24, 50, 1800, 5145, 878080, 3429216, 2857680000, 15219319500, 63117561830400, 457937132487120, 9577928124440387712, 94609025993497640625, 10077943267571584204800000

Offset: 1

Author

Labos Elemer, Jun 22 2001

Keywords

• easy
• nonn

Examples

			n=5: a(5) = 1*5*10 = 50;
n=6: a(6) = 1*6*15*20 = 1800. [corrected by _Jon E. Schoenfield_, Jul 01 2018]
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..97

Crossrefs

Cf. A001142, A001405.

Programs

GAP

List([1..20],n->Product([0..Int(n/2)],j->Binomial(n,j))); # Muniru A Asiru, Jul 01 2018

Mathematica

Table[Apply[Times, Table[Binomial[n, j], {j, 0, Floor[n/2]}]], {w, 1, 20}]
Table[Product[Binomial[n,j],{j,0,Floor[n/2]}],{n,20}] (* Harvey P. Dale, Dec 06 2018 *)

PARI

{ for (n=1, 97, write("b061778.txt", n, " ", prod(j=0, n\2, binomial(n, j))) ) } \\ Harry J. Smith, Jul 27 2009

Formula

For odd n, a(n) = sqrt(A001142(n)); for even n, (a(n)^2)/A001405(n) = A001142(n).