A192081 - OEIS

%I #33 Aug 02 2023 10:19:10

%S 1,1,18,86400,548674560000,14450101093977292800000,

%T 3837346984091658732083085312000000000,

%U 21256593329287301582222798129123366786826240000000000000,4543629380532096097361509541360459283717770305881596724510720000000000000000000

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

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

%H MathOverflow, <a href="http://mathoverflow.net/questions/77767/the-wronskian-of-sinkx-and-coskx-k1-n">The Wronskian of sin(kx) and cos(kx)</a>

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

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

%p a:= n-> mul((2*i-1)!, i=1..n)^2/n!:

%p seq(a(n), n=0..8);  # _Alois P. Heinz_, Aug 02 2023

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

%K nonn

%O 0,3

%A _Mark Sapir_, Oct 11 2011

%E a(0)=1 prepended by _Alois P. Heinz_, Aug 02 2023