%I #13 Sep 08 2022 08:45:06

%S 0,-1,-9,96,1250,-19440,-352947,7340032,172186884,-4500000000,

%T -129687123005,4086546038784,139788510734886,-5159146026151936,

%U -204350482177734375,8646911284551352320,389289535005334947848,-18580248257778920521728

%N Determinant of the Cayley addition table of Z_{n}.

%C a(n) is the determinant of the n X n matrix M_(i,j) = ((i+j) mod n) where i and j range from 0 to n-1. - _Benoit Cloitre_, Nov 29 2002

%C |a(n)| = number of labeled mappings from n points to themselves (endofunctions) with an even number of cycles. E.g.f.: (1/2)*LambertW(-x)^2/(1+LambertW(-x)). - _Vladeta Jovovic_, Mar 30 2006

%H G. C. Greubel, <a href="/A070896/b070896.txt">Table of n, a(n) for n = 1..385</a>

%F a(n) = (-1)^floor(n/2)*(1/2)*(n-1)*n^(n-1). - _Benoit Cloitre_, Nov 29 2002

%e a(3) = -9 because the determinant of {{0,1,2}, {1,2,0}, {2,0,1}} is -9.

%t Table[(-1)^Floor[n/2]*(1/2)*(n - 1)*n^(n - 1), {n, 1, 50}] (* _G. C. Greubel_, Nov 14 2017 *)

%o (PARI) a(n)=(-1)^floor(n/2)*(1/2)*(n-1)*n^(n-1)

%o (Magma) [(-1)^Floor(n/2)*(1/2)*(n-1)*n^(n-1): n in [1..50]]; // _G. C. Greubel_, Nov 14 2017

%Y Cf. A000312, A052182, A060281, A060435.

%K sign

%O 1,3

%A _Santi Spadaro_, May 23 2002