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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 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 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

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Last modified December 1 15:57 EST 2021. Contains 349430 sequences. (Running on oeis4.)