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Search: id:A097344
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| A097344 |
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Numerators in binomial transform of 1/(n+1)^2. |
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+0
4
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| 1, 5, 29, 103, 887, 1517, 18239, 63253, 332839, 118127, 2331085, 4222975, 100309579, 184649263, 1710440723, 6372905521, 202804884977, 381240382217, 13667257415003, 25872280345103, 49119954154463, 93501887462903, 4103348710010689, 7846225754967739, 75162749477272151
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Numerators in the expansion of ln((1-x)/(1-2x)) / (1-x) are 0,1,5,29,.. - Paul Barry (pbarry(AT)wit.ie), Feb 09 2005
Is this identical to A097345? - Aaron Gulliver, Jul 19 2007. The answer turns out to be No - see A134652.
If the putative formula a(n)=A081528(n) sum{k=0..n, binomial(n, k)/(k+1)^2} were true, then this sequence coincides with A097345 according to Mathar's notes. However, the term n=9 in the binomial transform of 1/(n+1)^2 has the denominator 5040=A081528(9)/4=A081528(10)/5. So the formula cannot be true. - M. F. Hasler, Jan 25 2008
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LINKS
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R. J. Mathar, Notes on an attempt to prove that A097344 and A097345 are identical
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EXAMPLE
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The first values of the binomial transform of 1/(n+1)^2 are 1, 5/4, 29/18, 103/48, 887/300, 1517/360, 18239/2940, 63253/6720, 332839/22680, 118127/5040, 2331085/60984, ...
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MAPLE
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f:=n->add( binomial(n, k)/(k+1)^2, k=0..n);
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PROGRAM
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(PARI) A097344(n)=numerator(sum(k=0, n, binomial(n, k)/(k+1)^2)) \\ - M. F. Hasler, Jan 25 2008
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CROSSREFS
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Cf. A097345, A134652.
Adjacent sequences: A097341 A097342 A097343 this_sequence A097345 A097346 A097347
Sequence in context: A050409 A111937 A097345 this_sequence A034700 A057721 A085151
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KEYWORD
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easy,nonn,frac
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Aug 06 2004
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EXTENSIONS
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Edited and corrected by Daniel Glasscock (glasscock(AT)rice.edu), Jan 04 2008, and M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jan 25 2008
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