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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*n-1) 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[n-1]*n!/Floor[n/2]!^2; Table[a[n], {n, 0, 14}] (* Jean-Fran├žois 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 * A037515 A037718 A020049

Adjacent sequences:  A163082 A163083 A163084 * A163086 A163087 A163088

KEYWORD

nonn

AUTHOR

Peter Luschny, Jul 21 2009

STATUS

approved

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Last modified August 20 17:05 EDT 2017. Contains 290836 sequences.