login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)^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)):

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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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