A118712 - OEIS

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A118712

a(n) = Determinant of n X n circulant matrix whose first row is A000001(1), A000001(2), ..., A000001(n) where A000001(n) = number of groups of order n.

1, 0, 0, -5, 6, -16, 9, -134400, 647248, -1711908, 6076067, -85248000, 116477425, -1764364437, 909276004, -522319050599375232, 14313181351994538493, -165893335414907083200, 2939566160282258664451, -5007637771411479278976, 75399747694572065660672 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,4`
	LINKS	`Table of n, a(n) for n=1..21.` `Eric Weisstein's World of Mathematics, Circulant Matrix.`
	EXAMPLE	`a(4) = -5 because of the determinant -5 =` `\|1,1,1,2\|` `\|2,1,1,1\|` `\|1,2,1,1\|` `\|1,1,2,1\|.` `a(11) = 6076067 = determinant` `\|1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1\|` `\|1, 1, 1, 1, 2, 1, 2, 1, 5, 2, 2\|` `\|2, 1, 1, 1, 1, 2, 1, 2, 1, 5, 2\|` `\|2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 5\|` `\|5, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1\|` `\|1, 5, 2, 2, 1, 1, 1, 1, 2, 1, 2\|` `\|2, 1, 5, 2, 2, 1, 1, 1, 1, 2, 1\|` `\|1, 2, 1, 5, 2, 2, 1, 1, 1, 1, 2\|` `\|2, 1, 2, 1, 5, 2, 2, 1, 1, 1, 1\|` `\|1, 2, 1, 2, 1, 5, 2, 2, 1, 1, 1\|` `\|1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 1\|.`
	PROG	`(GAP) A118712 := n -> DeterminantMat(List([0..n-1], i->List([0..n-1], j->NrSmallGroups(((j-i) mod n)+1)))); # Eric M. Schmidt, Nov 17 2013`
	CROSSREFS	`Cf. A000001, A048954, A052182, A066933, A086459, A086569.` `Sequence in context: A019071 A028285 A007430 * A130878 A104422 A026547` `Adjacent sequences: A118709 A118710 A118711 * A118713 A118714 A118715`
	KEYWORD	`sign`
	AUTHOR	`Jonathan Vos Post, May 20 2006`
	EXTENSIONS	`a(1) corrected by and more terms from Eric M. Schmidt, Nov 17 2013`
	STATUS	`approved`

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Last modified March 31 08:44 EDT 2023. Contains 361645 sequences. (Running on oeis4.)