A163085 Product of first n swinging factorials (A056040).

1, 1, 2, 12, 72, 2160, 43200, 6048000, 423360000, 266716800000, 67212633600000, 186313420339200000, 172153600393420800000, 2067909047925770649600000, 7097063852481244869427200000

Offset: 0

Author

Peter Luschny, Jul 21 2009

Keywords

• nonn

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

Crossrefs

Cf. A056040, A163086, A055462, A000178.

Programs

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 *)

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