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A070896 Determinant of the Cayley addition table of Z_{n}. 7
0, -1, -9, 96, 1250, -19440, -352947, 7340032, 172186884, -4500000000, -129687123005, 4086546038784, 139788510734886, -5159146026151936, -204350482177734375, 8646911284551352320, 389289535005334947848, -18580248257778920521728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

Cf. A000312, A052182, A060281, A060435.

Sequence in context: A024116 A264208 * A081131 A158489 A069636 A069621

Adjacent sequences:  A070893 A070894 A070895 * A070897 A070898 A070899

KEYWORD

sign

AUTHOR

Santi Spadaro, May 23 2002

STATUS

approved

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Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)