A070896 Determinant of the Cayley addition table of Z_{n}.

0, -1, -9, 96, 1250, -19440, -352947, 7340032, 172186884, -4500000000, -129687123005, 4086546038784, 139788510734886, -5159146026151936, -204350482177734375, 8646911284551352320, 389289535005334947848, -18580248257778920521728

Offset: 1

Author

Santi Spadaro, May 23 2002

Keywords

• sign

Comments

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

|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

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..385

Crossrefs

Cf. A000312, A052182, A060281, A060435.

Programs

Magma

[(-1)^Floor(n/2)*(1/2)*(n-1)*n^(n-1): n in [1..50]]; // G. C. Greubel, Nov 14 2017

Mathematica

Table[(-1)^Floor[n/2]*(1/2)*(n - 1)*n^(n - 1), {n, 1, 50}] (* G. C. Greubel, Nov 14 2017 *)

PARI

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

Formula

a(n) = (-1)^floor(n/2)*(1/2)*(n-1)*n^(n-1). - Benoit Cloitre, Nov 29 2002