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Search: id:A119537
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| A119537 |
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Determinant of n X n matrices of first n^2 denumerants (A000115). |
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+0
1
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| 1, 0, -3, -3, 0, -54, 343, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Conjecture: a(n>7)=0. - from Robert G. Wilson v (rgwv(at)rgwv.com),Jun 07 2006
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FORMULA
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a(n) = determinant[A000115(k) from k=1 to n^2)].
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EXAMPLE
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a(6) = -54 = -2 * 3^3. a(7) = 343 = 7^3.
a(8) = 0 because of the singular matrix 0 =
|..1...1...2...2...3...4...5...6|
|..7...8..10..11..13..14..16..18|
|.20..22..24..26..29..31..34..36|
|.39..42..45..48..51..54..58..61|
|.65..68..72..76..80..84..88..92|
|.97.101.106.110.115.120.125.130|
|135.140.146.151.157.162.168.174|
|180.186.192.198.205.211.218.224|.
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MATHEMATICA
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clst = CoefficientList[ Series[1/((1 - x)(1 - x^2)(1 - x^5)), {x, 0, 105^2 - 1}], x]; f[n_] := Det[ Partition[ Take[clst, n^2], n]]; Array[f, 100] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000115, A119493.
Sequence in context: A039928 A137259 A111843 this_sequence A031438 A096964 A123254
Adjacent sequences: A119534 A119535 A119536 this_sequence A119538 A119539 A119540
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KEYWORD
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easy,sign
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 28 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com),Jun 07 2006
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