A085524 a(0) = 0; a(n) = n^(2*n-1) for n > 0.

0, 1, 8, 243, 16384, 1953125, 362797056, 96889010407, 35184372088832, 16677181699666569, 10000000000000000000, 7400249944258160101211, 6624737266949237011120128, 7056410014866816666030739693, 8819763977946281130444984418304, 12783403948858939111232757568359375

Offset: 0

Author

N. J. A. Sloane, Jul 05 2003

Keywords

• nonn

Comments

For n > 0, a(n) is the square of the determinant of the (2*n) X (2*n) matrix with elements M(j,k) = cos(Pi*j*k/n). See the MathOverflow link. - Hugo Pfoertner, Sep 18 2021

Links

• Joerg Arndt, Table of n, a(n) for n = 0..100
• Zhi-Wei Sun, Fedor Petrov, A surprising identity, discussion in MathOverflow, Jan 17 2019.

Crossrefs

Cf. A062206, A085526, A089072.

Programs

Magma

[n eq 0 select 0 else n^(2*n-1): n in [0..30]]; // G. C. Greubel, Nov 01 2022

Mathematica

Join[{0}, Table[n^(2 n - 1), {n, 20}]] (* Harvey P. Dale, May 16 2016 *)

PARI

a(n) = if(n==0, 0, n^(2*n-1)) \\ Altug Alkan, Oct 04 2017

SageMath

[0]+[n^(2*n-1) for n in range(1,31)] # G. C. Greubel, Nov 01 2022

Formula

a(n) = n! * [x^n] -LambertW(-n*x). - Ilya Gutkovskiy, Oct 04 2017

a(n) = A089072(2*n-1, n), n >= 1. - G. C. Greubel, Nov 01 2022