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!)
A324361 Total number of occurrences of n in the (signed) displacement sets of all permutations of [2n] divided by n!. 3
0, 1, 5, 49, 679, 12151, 266321, 6906257, 206788751, 7020426511, 266464077769, 11180868467209, 513915970996583, 25678820830238759, 1385874945753239969, 80341660921985676961, 4979071555472111291551, 328496221117149603559327, 22987138271050177264124441 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..366

Wikipedia, Permutation

FORMULA

a(n) = n! [x^n] (1-exp(-x))/(1-x)^(n+1).

a(n) = -1/n! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (2n-j)!.

a(n) = (8*n-12)*a(n-1) - (16*n^2-64*n+59)*a(n-2) - (4*n-10)*a(n-3) for n > 2.

a(n) = A324362(n,n) = A306234(2n,n).

MAPLE

a:= proc(s) option remember; `if`(n<3, (3*n-1)*n/2,

      (8*n-12)*a(n-1)-(16*n^2-64*n+59)*a(n-2)-(4*n-10)*a(n-3))

    end:

seq(a(n), n=0..20);

CROSSREFS

Main diagonal of A324362.

Cf. A000142, A306234.

Sequence in context: A297513 A228511 A116873 * A089914 A267220 A052142

Adjacent sequences:  A324358 A324359 A324360 * A324362 A324363 A324364

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 23 2019

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 January 20 07:11 EST 2021. Contains 340301 sequences. (Running on oeis4.)