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A281262
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Number of permutations of [2n] with exactly n fixed points.
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3
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1, 0, 6, 40, 630, 11088, 244860, 6362928, 190900710, 6490575520, 246642054516, 10358965584240, 476512419579196, 23825620968559200, 1286583532342313400, 74621844875699059680, 4626554382293942780550, 305352589231397889910080, 21374681246197861368840900
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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) = (4*n-2)*((n-1)*a(n-1)+(4*n-6)*a(n-2))/n for n>1, a(n) = 1-n for n<2.
a(n) = binomial(2n,n) * A000166(n).
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EXAMPLE
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a(2) = 6: 1243, 1324, 1432, 2134, 3214, 4231.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 1-n,
(4*n-2)*((n-1)*a(n-1)+(4*n-6)*a(n-2))/n)
end:
seq(a(n), n=0..20);
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MATHEMATICA
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a[n_] := Binomial[2n, n] Subfactorial[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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