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A199660
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Number of parity alternating permutations of [n] avoiding descents from odd to even numbers.
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5
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1, 1, 2, 1, 5, 2, 20, 6, 114, 24, 864, 120, 8280, 720, 96480, 5040, 1325520, 40320, 20966400, 362880, 374855040, 3628800, 7468070400, 39916800, 163938297600, 479001600, 3929729126400, 6227020800, 102104460057600, 87178291200, 2857878742118400, 1307674368000
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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(0) = 1, a(2*n) = (2^n+n-1)*(n-1)! for n>0, a(2*n+1) = n!.
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EXAMPLE
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a(4) = 5: (1,2,3,4), (2,1,4,3), (2,3,4,1), (3,4,1,2), (4,1,2,3).
a(5) = 2: (1,2,3,4,5), (3,4,1,2,5).
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MAPLE
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a:= n-> `if`(n=0, 1, `if`(irem(n, 2, 'r')=0, (2^r+r-1)*(r-1)!, r!)):
seq(a(n), n=0..35);
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MATHEMATICA
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a[n_] := If[n == 0, 1, With[{r = Quotient[n, 2]},
If[Mod[n, 2] == 0, (2^r+r-1)(r-1)!, r!]]];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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