A192081 Wronskian of sin(k*x) and cos(k*x), k=1,...,n.
1, 1, 18, 86400, 548674560000, 14450101093977292800000, 3837346984091658732083085312000000000, 21256593329287301582222798129123366786826240000000000000, 4543629380532096097361509541360459283717770305881596724510720000000000000000000
Offset: 0
Keywords
Examples
a(3) = (1*6*120)^2/6 = 86400.
Links
- MathOverflow, The Wronskian of sin(kx) and cos(kx)
Programs
-
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 *)
Formula
a(n) = (1! * 3! * ... * (2n-1)!)^2/n!.
Extensions
a(0)=1 prepended by Alois P. Heinz, Aug 02 2023
Comments