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!)
A273325 Number of endofunctions on [2n] such that the minimal cardinality of the nonempty preimages equals n. 2
1, 2, 36, 300, 1960, 11340, 60984, 312312, 1544400, 7438860, 35103640, 162954792, 746347056, 3380195000, 15164074800, 67476121200, 298135873440, 1309153089420, 5717335239000, 24847720451400, 107520292479600, 463440029892840, 1990477619679120, 8521600803066000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(0) = 1 by convention.
LINKS
FORMULA
G.f.: 1+(8*x+1)*2*x/(1-4*x)^(5/2).
a(n) = C(2*n,n)*C(2*n,2) for n>0, a(0)=1.
a(n) = 2*C(2*(n-1),n-1)*(2*n-1)^2, a(0)=1.
a(n) = 2*(2*n-1)^2*a(n-1)/((n-1)*(2*n-3)) for n>1, a(n) = 2^n for n=0..1.
a(n) = A245687(2n,n).
a(n) = A000108(n)*A213820(n) = 2*A000108(n)*A002414(n) for n>0, a(0)=1.
Sum_{n>=0} 1/a(n) = 1 - log(sqrt(3)+2)*Pi/6 + 4*G/3, where G is Catalan's constant (A006752). - Amiram Eldar, Mar 12 2023
EXAMPLE
a(1) = 2: 12, 21.
a(2) = 36: 1122, 1133, 1144, 1212, 1221, 1313, 1331, 1414, 1441, 2112, 2121, 2211, 2233, 2244, 2323, 2332, 2424, 2442, 3113, 3131, 3223, 3232, 3311, 3322, 3344, 3434, 3443, 4114, 4141, 4224, 4242, 4334, 4343, 4411, 4422, 4433.
MAPLE
a:= proc(n) option remember; `if`(n<2, 2^n,
2*(2*n-1)^2*a(n-1)/((n-1)*(2*n-3)))
end:
seq(a(n), n=0..30);
MATHEMATICA
a[n_] := (2*n^3 + n^2 - n) * CatalanNumber[n]; a[0] = 1; Array[a, 30, 0] (* Amiram Eldar, Mar 12 2023 *)
CROSSREFS
Sequence in context: A074426 A082636 A242533 * A035603 A126735 A229679
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, May 20 2016
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 June 16 11:31 EDT 2024. Contains 373429 sequences. (Running on oeis4.)