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!)
A245141 Number of endofunctions f on [2n] that are self-inverse on [n]. 3
1, 3, 50, 1626, 83736, 6026120, 571350096, 67996818960, 9862902275456, 1700092943088768, 342087177215788800, 79115601821198404352, 20779757607847901690880, 6133520505473954148381696, 2017134796016735182500521984, 733523863838078950241395968000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) counts endofunctions f:{1,...,2n}-> {1,...,2n} with f(f(i))=i for all i in {1,...,n}.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) = Sum_{i=0..n} C(n,i)^2 * i! * A000085(n-i) * (2*n)^(n-i).

a(n) = A245348(2n,n).

EXAMPLE

a(1) = 3: (1,1), (1,2), (2,1).

MAPLE

g:= proc(n) g(n):= `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:

a:= n-> add(binomial(n, i)^2*i!*g(n-i)*(2*n)^(n-i), i=0..n):

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

CROSSREFS

Cf. A000085, A245348.

Column k=2 of A246070.

Sequence in context: A246283 A326250 A308331 * A203239 A279970 A217767

Adjacent sequences:  A245138 A245139 A245140 * A245142 A245143 A245144

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 21 2014

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 September 25 22:55 EDT 2020. Contains 337346 sequences. (Running on oeis4.)