OFFSET
0,3
COMMENTS
With the definition of the Hankel transform as given by Luschny (see link) which uniquely determines the original sequence (provided that all determinants are not zero) this is also 1/ the Hankel determinant of 1/(n+1) (assuming (0,0)-based matrices).
a(2*n-1) is 1/determinant of the Hilbert matrix H(n) (A005249).
a(2*n) = A067689(n). - Peter Luschny, Sep 18 2012
LINKS
Peter Luschny, SequenceTransformations
MAPLE
a := proc(n) local i; mul(A056040(i), i=0..n) end;
MATHEMATICA
a[0] = 1; a[n_] := a[n] = a[n-1]*n!/Floor[n/2]!^2; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Jun 26 2013 *)
PROG
(Sage)
def A056040(n):
swing = lambda n: factorial(n)/factorial(n//2)^2
return mul(swing(i) for i in (0..n))
[A056040(i) for i in (0..14)] # Peter Luschny, Sep 18 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 21 2009
STATUS
approved