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A085524 a(0) = 0; a(n) = n^(2*n-1) for n > 0. 4
0, 1, 8, 243, 16384, 1953125, 362797056, 96889010407, 35184372088832, 16677181699666569, 10000000000000000000, 7400249944258160101211, 6624737266949237011120128, 7056410014866816666030739693, 8819763977946281130444984418304, 12783403948858939111232757568359375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

FORMULA

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A062206, A085526.

Sequence in context: A229544 A115613 A209540 * A062481 A053089 A090241

Adjacent sequences:  A085521 A085522 A085523 * A085525 A085526 A085527

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 05 2003

STATUS

approved

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Last modified December 1 07:59 EST 2021. Contains 349426 sequences. (Running on oeis4.)