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A070896
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Determinant of the Cayley addition table of Z_{n}.
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5
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0, -1, -9, 96, 1250, -19440, -352947, 7340032, 172186884, -4500000000, -129687123005, 4086546038784, 139788510734886, -5159146026151936, -204350482177734375, 8646911284551352320, 389289535005334947848, -18580248257778920521728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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 (benoit7848c(AT)orange.fr), 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 (vladeta(AT)eunet.rs), Mar 30 2006
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FORMULA
| a(n) = (-1)^floor(n/2)*(1/2)*(n-1)*n^(n-1). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 29 2002
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EXAMPLE
| a(3)=-9 because the determinant of {{0,1,2}, {1,2,0}, {2,0,1}} is -9.
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PROG
| (PARI) a(n)=(-1)^floor(n/2)*(1/2)*(n-1)*n^(n-1)
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CROSSREFS
| Cf. A000312, A052182, A060281, A060435.
Sequence in context: A069055 A024116 * A081131 A158489 A069636 A069621
Adjacent sequences: A070893 A070894 A070895 * A070897 A070898 A070899
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KEYWORD
| sign
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AUTHOR
| Santi Spadaro (spados(AT)katamail.com), May 23 2002
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