

A163085


Product of first n swinging factorials (A056040).


9



1, 1, 2, 12, 72, 2160, 43200, 6048000, 423360000, 266716800000, 67212633600000, 186313420339200000, 172153600393420800000, 2067909047925770649600000, 7097063852481244869427200000
(list;
graph;
refs;
listen;
history;
text;
internal format)



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*n1) is 1/determinant of the Hilbert matrix H(n) (A005249).
a(2*n) = A067689(n).  Peter Luschny, Sep 18 2012


LINKS

Table of n, a(n) for n=0..14.
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[n1]*n!/Floor[n/2]!^2; Table[a[n], {n, 0, 14}] (* JeanFrançois 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

Cf. A056040, A163086, A055462, A000178.
Sequence in context: A235359 A130426 A002397 * A328946 A037515 A037718
Adjacent sequences: A163082 A163083 A163084 * A163086 A163087 A163088


KEYWORD

nonn


AUTHOR

Peter Luschny, Jul 21 2009


STATUS

approved



