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A070896 Determinant of the Cayley addition table of Z_{n}. 10
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
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
Sequence in context: A024116 A264208 A357209 * A081131 A338105 A331113
KEYWORD
sign
AUTHOR
Santi Spadaro, May 23 2002
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)