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!)
A085530 a(n) = (2n+1)^(2n). 4
1, 9, 625, 117649, 43046721, 25937424601, 23298085122481, 29192926025390625, 48661191875666868481, 104127350297911241532841, 278218429446951548637196401, 907846434775996175406740561329, 3552713678800500929355621337890625, 16423203268260658146231467800709255289 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n)/4^n is the square of the determinant of a (2*n+1) X (2*n+1) matrix with elements M(j,k) = cos(Pi*j*k/n). See the MathOverflow link. - Hugo Pfoertner, Sep 18 2021
LINKS
Zhi-Wei Sun, Fedor Petrov, A surprising identity, discussion in MathOverflow, Jan 17 2019.
FORMULA
From Mathew Englander, Aug 14 2020: (Start)
a(n) = A085527(n)^2.
a(n) = A085529(n)/(2*n + 1).
(End)
From Alois P. Heinz, Aug 14 2020: (Start)
a(n) = A016754(n)^n.
a(n) = A005408(n)^A005843(n). (End)
MATHEMATICA
Table[(2 n + 1)^(2 n), {n, 0, 20}] (* Vincenzo Librandi, Feb 26 2013 *)
PROG
(Magma) [(2*n+1)^(2*n): n in [0..13]]; // Vincenzo Librandi, Feb 26 2013
CROSSREFS
Sequence in context: A277232 A171703 A352276 * A188423 A158881 A188394
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 05 2003
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 March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)