A085530 a(n) = (2n+1)^(2n).

1, 9, 625, 117649, 43046721, 25937424601, 23298085122481, 29192926025390625, 48661191875666868481, 104127350297911241532841, 278218429446951548637196401, 907846434775996175406740561329, 3552713678800500929355621337890625, 16423203268260658146231467800709255289

Offset: 0

Author

N. J. A. Sloane, Jul 05 2003

Keywords

• nonn
• easy

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

• Vincenzo Librandi, Table of n, a(n) for n = 0..190
• Zhi-Wei Sun, Fedor Petrov, A surprising identity, discussion in MathOverflow, Jan 17 2019.

Crossrefs

Cf. A005408, A005843, A016754, A085527, A085529.

Programs

Magma

[(2*n+1)^(2*n): n in [0..13]]; // Vincenzo Librandi, Feb 26 2013

Mathematica

Table[(2 n + 1)^(2 n), {n, 0, 20}] (* Vincenzo Librandi, Feb 26 2013 *)

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)