A192081 Wronskian of sin(k*x) and cos(k*x), k=1,...,n.

1, 1, 18, 86400, 548674560000, 14450101093977292800000, 3837346984091658732083085312000000000, 21256593329287301582222798129123366786826240000000000000, 4543629380532096097361509541360459283717770305881596724510720000000000000000000

Offset

0,3

Comments

a(n) is the Wronskian of functions {cos(x), sin(x), cos(2x), sin(2x), ..., cos(n*x), sin(n*x)}.

Links

Table of n, a(n) for n=0..8.

MathOverflow, The Wronskian of sin(kx) and cos(kx)

Formula

a(n) = (1! * 3! * ... * (2n-1)!)^2/n!.

Example

a(3) = (1*6*120)^2/6 = 86400.

Maple

a:= n-> mul((2*i-1)!, i=1..n)^2/n!:
seq(a(n), n=0..8);  # Alois P. Heinz, Aug 02 2023

Mathematica

s = 1; Join[{s}, Table[s=s*((2*n-1)!)^2/n, {n, 2, 7}]] (* T. D. Noe, Oct 11 2011 *)

Crossrefs

Sequence in context: A146548 A051591 A146203 * A290177 A259364 A013762

Adjacent sequences: A192078 A192079 A192080 * A192082 A192083 A192084

Keyword

nonn

Author

Mark Sapir, Oct 11 2011

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 02 2023

Status

approved