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Search: id:A099325
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| A099325 |
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Expansion of (sqrt(1+2x)+sqrt(1-2x))/(2(1-2x)^(3/2)). |
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+0
3
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| 1, 3, 7, 16, 35, 76, 162, 344, 723, 1516, 3158, 6568, 13598, 28120, 57956, 119344, 245123, 503116, 1030542, 2109704, 4311786, 8808328, 17969372, 36644176, 74640430, 151985016, 309170332, 628741264, 1277540828, 2595198256
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The g.f. is transformed to 1/(1-x)^3 under the Chebyshev transformation A(x)->1/(1+x^2)A(x/(1+x^2)). Second binomial transform of the sequence with g.f. 1/c(-x), where c(x) is the g.f. of the Catalan numbers A000108.
Image of 2n+1 under the Riordan array (1/sqrt(1-4x^2),xc(x^2)). Hankel transform is (n+1)*(-1)^n. - Paul Barry (pbarry(AT)wit.ie), Oct 06 2007
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FORMULA
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a(n)=sum{k=0..n, (k+1)binomial(n, (n-k)/2)binomial(k+2, 2)(1+(-1)^(n-k))/(n+k+2)}.
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CROSSREFS
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Cf. A099326, A099327.
Sequence in context: A133124 A104004 A101509 this_sequence A026778 A023523 A065979
Adjacent sequences: A099322 A099323 A099324 this_sequence A099326 A099327 A099328
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 12 2004
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