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 A088335 Number of permutations in the symmetric group S_n such that the size of their centralizer is even. 2
 0, 0, 2, 4, 16, 96, 576, 4320, 31872, 298368, 3052800, 34387200, 404029440, 5339473920, 75893207040, 1139356108800, 18079668633600, 310896849715200, 5654417758617600, 107707364764876800, 2145784566959308800, 45252164164799692800, 1003024255355781120000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 FORMULA a(n) = n! - A088994(n). MAPLE b:= proc(n, i) option remember; `if`(((i+1)/2)^2n, 0, (i-1)!*        b(n-i, i-2)*binomial(n, i))))     end: a:= n-> n!-b(n, n-1+irem(n, 2)): seq(a(n), n=0..30);  # Alois P. Heinz, Jan 27 2020 MATHEMATICA 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]]; a /@ Range[0, 30] (* Jean-François Alcover, Apr 08 2020, after Alois P. Heinz *) PROG (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 CROSSREFS Cf. A000142, A088994. Sequence in context: A052835 A009565 A009838 * A066318 A308606 A066952 Adjacent sequences:  A088332 A088333 A088334 * A088336 A088337 A088338 KEYWORD nonn AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 07 2003 EXTENSIONS a(0)=0 prepended and terms a(11) and beyond from Andrew Howroyd, Jan 27 2020 STATUS approved

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Last modified May 25 20:52 EDT 2020. Contains 334595 sequences. (Running on oeis4.)