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A363180
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Number of permutations of [2n] with n parity changes.
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3
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1, 2, 8, 288, 10368, 1036800, 103680000, 20321280000, 3982970880000, 1290482565120000, 418116351098880000, 202368313931857920000, 97946263943019233280000, 66211674425481001697280000, 44759091911625157147361280000, 40283182720462641432625152000000
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OFFSET
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0,2
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LINKS
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FORMULA
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Recurrence: (2*n - 3)*a(n) = 4*(2*n^2 - 4*n + 1)*a(n-1) + 16*(n-2)^2*(n-1)^2*(2*n - 1)*a(n-2).
a(n) ~ 2^(2*n+1) * n^(2*n) / exp(2*n). (End)
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EXAMPLE
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a(0) = 1: (), the empty permutation.
a(1) = 2: 12, 21.
a(2) = 8: 1243, 1423, 2134, 2314, 3241, 3421, 4132, 4312.
a(3) = 288: 123546, 123564, 124356, 124536, 125346, ..., 652431, 653241, 653421, 654213, 654231.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 2^n,
(16*(n-2)^2*(2*n-1)*(n-1)^2*a(n-2)+4*(2*n^2-4*n+1)*a(n-1))/(2*n-3))
end:
seq(a(n), n=0..18);
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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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