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

1,2

Links

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

Formula

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

Example

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]

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 *)

Prog

(PARI) { for (n=1, 97, write("b061778.txt", n, " ", prod(j=0, n\2, binomial(n, j))) ) } \\ Harry J. Smith, Jul 27 2009
(GAP) List([1..20], n->Product([0..Int(n/2)], j->Binomial(n, j))); # Muniru A Asiru, Jul 01 2018

Crossrefs

Cf. A001142, A001405.

Sequence in context: A377825 A336616 A354278 * A160667 A118204 A061355

Adjacent sequences: A061775 A061776 A061777 * A061779 A061780 A061781

Keyword

easy,nonn

Author

Labos Elemer, Jun 22 2001

Status

approved