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Search: id:A085840
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| A085840 |
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Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / [ (2n-2m+1)! (2m)! ]. |
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3
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| 1, 1, 12, 1, 40, 80, 1, 84, 560, 448, 1, 144, 2016, 5376, 2304, 1, 220, 5280, 29568, 42240, 11264, 1, 312, 11440, 109824, 329472, 292864, 53248, 1, 420, 21840, 320320, 1647360, 3075072, 1863680, 245760
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row #n has the unsigned coefficients of a polynomial whose roots are 2 tan (pi k / (2n+1)) [for k=1 to 2n].
Polynomial of row #n = sum(m=0 to n) [(-1)^m] T(n,m) x^(2n-2m).
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EXAMPLE
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1
x^2 - 12
x^4 - 40x^2 + 80
x^6 - 84x^4 + 560x^2 - 448
x^8 - 144x^6 + 2016x^4 - 5376x^2 + 2304
x^10 - 220x^8 + 5280x^6 - 29568x^4 + 42240x^2 - 11264
Polynomial #4 has eight roots: 2 tan (pi k / 9) for k=1 to 8.
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CROSSREFS
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Cf. A085841.
Sequence in context: A036185 A013619 A092527 this_sequence A075072 A038327 A157780
Adjacent sequences: A085837 A085838 A085839 this_sequence A085841 A085842 A085843
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 05 2003
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Nov 13 2005
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