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Search: id:A129326
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| 3, 5, 14, 54, 264, 1560, 10800, 85680, 766080, 7620480, 83462400, 997920000, 12933043200, 180583603200, 2702527027200, 43153254144000, 732297646080000, 13160434839552000, 249692574523392000, 4987449116762112000, 104614786351595520000, 2299092397726924800000
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OFFSET
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1,1
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COMMENT
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In 1998, with help of planar polynomial differential systems, I discovered three bidimensional polynomials. Two of them are odd, the third, based on a degenerate case, is normal. In one dimension, it can be written D(n,z) = sum[((n+2)^2-(i+1)^2)*z/(i+1)] i=0..n Its roots are all complex when n is even and all except one if n is odd. They are equally distributed (thanks to Jean-Charles Faugare [Faugere?] in 2000). We write the first 4 lines and the transformed terms after multiplication by n!
.........3........................................3
.........8..5/2..................................16.....5
........15..12/2...7/3...........................90....36...14
........24..21/2..16/3..9/4.....................576...252..128..54.....
The numerators of the columns of the first array are well known (A005563, A028347, A028360). But the first vertical sequence and the one of the highest diagonal of the second array are unknown.
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FORMULA
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a(n)=A052649(n), n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 14 2008
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CROSSREFS
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Sequence in context: A006395 A078718 A081393 this_sequence A118562 A115043 A058220
Adjacent sequences: A129323 A129324 A129325 this_sequence A129327 A129328 A129329
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), May 26 2007
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EXTENSIONS
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More terms from njas, Nov 08 2007
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