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A161122
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Number of cycles with entries of the same parity in all fixed-point-free involutions of {1,2,...,2n}.
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4
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0, 0, 2, 18, 180, 2100, 28350, 436590, 7567560, 145945800, 3101348250, 72020198250, 1814908995900, 49332526343100, 1438865351673750, 44826189802143750, 1485668004871050000, 52196469237802890000, 1937793920453432291250, 75801938653031321981250, 3116301922402398792562500
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n(n-1)(2n-3)!!.
D-finite with recurrence (-n+2)*a(n) +n*(2*n-3)*a(n-1)=0. - R. J. Mathar, Jul 26 2022
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EXAMPLE
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a(2)=2 because in the 3 permutations (12)(34), (13)(24), (14)(23) we have a total of 2 cycles with entries of the same parity.
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MAPLE
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seq(n*(n-1)*(product(2*j-1, j = 1 .. n-1)), n = 0 .. 18);
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MATHEMATICA
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PROG
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(Magma) DoubleFactorial:=func< n | &*[n..2 by -2] >; [ n*(n-1)*DoubleFactorial(2*n-3): n in [0..22]]; // Vincenzo Librandi, Jul 21 2017
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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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