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Search: id:A126224
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| A126224 |
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Determinant of the n X n matrix in which the entries are 1 through n^2, spiraling inward starting with 1 in the (1,1)-entry. |
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+0
1
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| 1, -5, -48, 660, 11760, -257040, -6652800, 198918720, 6745939200, -255826771200, -10727081164800, 492775291008000, 24610605962342400, -1327677426915840000, -76940526008586240000, 4766815315895592960000, 314406967644177408000000
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Sergey Sadov, Problem 11270, American Mathematical Monthly, Vol. 114, No. 1, 2007, p. 78.
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FORMULA
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a(n)=(-1)^[n(n-1)/2]*2^(2n-3)*(3n-1)*Product(1/2+k, k=0..n-2) for n>=2.
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EXAMPLE
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a(2)=-5 because det(matrix(1,2 / 4,3)=3-8=-5.
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MAPLE
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a:=n->(-1)^(n*(n-1)/2)*2^(2*n-3)*(3*n-1)*product(1/2+k, k=0..n-2): seq(a(n), n=1..20);
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CROSSREFS
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Sequence in context: A116431 A048435 A023999 this_sequence A108207 A127091 A063429
Adjacent sequences: A126221 A126222 A126223 this_sequence A126225 A126226 A126227
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KEYWORD
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sign
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 31 2006
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