The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A246050 Number of endofunctions on [2n] where the smallest cycle length equals n. 4
1, 3, 51, 4360, 861420, 302472576, 165549605760, 130241382036480, 139296260790086400, 194427690066299289600, 343266609438110040883200, 747889929370001008617062400, 1971026055567996899374212710400, 6180432763819774878006029844480000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = A246049(2n,n) = A243098(2n,n).
a(n) ~ 2^(3*n-1/2) * n^(2*n-1) / exp(n). - Vaclav Kotesovec, Aug 19 2014
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i+1), j=0..n/i)))
end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
a:= n-> `if`(n=0, 1, A(2*n, n) -A(2*n, n+1)):
seq(a(n), n=0..15);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i>n, 0, Sum[(i-1)!^j*multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*b[n-i*j, i+1], {j, 0, n/i}]]]; A[n_, k_] := Sum[Binomial[n-1, j-1]*n^(n-j)*b[j, k], {j, 0, n}]; a[n_] := If[n == 0, 1, A[2*n, n] - A[2*n, n+1]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 11 2015, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A069343 A084882 A275798 * A091502 A307022 A330302
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 11 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 12:09 EDT 2024. Contains 372773 sequences. (Running on oeis4.)