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A088335
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Number of permutations in the symmetric group S_n such that the size of their centralizer is even.
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2
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0, 0, 2, 4, 16, 96, 576, 4320, 31872, 298368, 3052800, 34387200, 404029440, 5339473920, 75893207040, 1139356108800, 18079668633600, 310896849715200, 5654417758617600, 107707364764876800, 2145784566959308800, 45252164164799692800, 1003024255355781120000
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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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MAPLE
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b:= proc(n, i) option remember; `if`(((i+1)/2)^2<n, 0,
`if`(n=0, 1, b(n, i-2)+`if`(i>n, 0, (i-1)!*
b(n-i, i-2)*binomial(n, i))))
end:
a:= n-> n!-b(n, n-1+irem(n, 2)):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[((i + 1)/2)^2 < n, 0, If[n == 0, 1, b[n, i - 2] + If[i > n, 0, (i - 1)! b[n - i, i - 2] Binomial[n, i]]]];
a[n_] := n! - b[n, n - 1 + Mod[n, 2]];
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PROG
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(PARI) seq(n)={Vec(serlaplace(1/(1-x) - prod(k=1, n, 1+(k%2)*x^k/k + O(x*x^n))), -(n+1))} \\ Andrew Howroyd, Jan 27 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 07 2003
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EXTENSIONS
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a(0)=0 prepended and terms a(11) and beyond from Andrew Howroyd, Jan 27 2020
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STATUS
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approved
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