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A163085
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Product of first n swinging factorials (A056040).
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9
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1, 1, 2, 12, 72, 2160, 43200, 6048000, 423360000, 266716800000, 67212633600000, 186313420339200000, 172153600393420800000, 2067909047925770649600000, 7097063852481244869427200000
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OFFSET
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0,3
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COMMENTS
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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).
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LINKS
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MAPLE
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a := proc(n) local i; mul(A056040(i), i=0..n) end;
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MATHEMATICA
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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 *)
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PROG
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(Sage)
swing = lambda n: factorial(n)/factorial(n//2)^2
return mul(swing(i) for i in (0..n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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