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Search: id:A100087
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| A100087 |
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Expansion of x/(sqrt(1-4x^2)+x-1). |
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+0
3
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| 1, 2, 4, 10, 24, 60, 148, 370, 920, 2300, 5736, 14340, 35808, 89520, 223668, 559170, 1397496, 3493740, 8732920, 21832300, 54575888, 136439720, 341082504, 852706260, 2131706864, 5329267160, 13322959888, 33307399720, 83267756400
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Inverse Chebyshev transform of (1-x^2)/((1-2x)(1+x^2)), the g.f. of A100088, under the mapping g(x)->(1/sqrt(1-4x^2))g(xc(x^2)) where c(x) is the g.f. of the Catalan numbers A000108. Equivalently, its image under the Chebyshev map A(x)->((1-x^2)/(1+x^2))A(x/(1+x^2)) is A100088.
Transform of 1/(1-2x) under the mapping g(x)->g(xc(x^2)). - Paul Barry (pbarry(AT)wit.ie), Jan 17 2005
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FORMULA
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a(n)=sum{k=0..floor(n/2), C(n, k)(3*2^(n-2k)+2cos(pi*(n-2k)/2)+4sin(pi*(n-2k)/2))/5}; a(n)=sum{k=0..floor(n/2), C(n, k)A100088(n-2k)}.
a(n)=sum{k=0..n, k*binomial(n-1, (n-k)/2)(1+(-1)^(n-k))2^k/(n+k)}; - Paul Barry (pbarry(AT)wit.ie), Jan 17 2005
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CROSSREFS
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Adjacent sequences: A100084 A100085 A100086 this_sequence A100088 A100089 A100090
Sequence in context: A065161 A038373 A052987 this_sequence A088354 A055919 A006575
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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), Nov 03 2004
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