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A155084
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A Catalan transform of [x^n](1/(1-2x-2x^2)) (A002605).
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1
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1, 2, 8, 32, 132, 552, 2328, 9872, 42020, 179336, 766888, 3284272, 14081224, 60426576, 259490736, 1114965792, 4792924356, 20611174920, 88662405768, 381494338032, 1641837542232, 7067257125744, 30425523536592
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OFFSET
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0,2
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COMMENTS
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Hankel transform is 4^n.
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LINKS
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FORMULA
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G.f.: 1/(1-2x*c(x)-2(x*c(x))^2), where c(x) is the g.f. of A000108.
G.f.: 1/(1-2x-4x^2/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-..... (continued fraction).
a(n) = Sum_{k=0..n} (k/(2n-k))*binomial(2n-k, n-k)*A002605(k), a(0) = 1.
Apparently 3*n*a(n) +6*(3-4*n)*a(n-1) +4*(11*n-18)*a(n-2) +8*(2*n-3)*a(n-3)=0. - R. J. Mathar, Oct 25 2012
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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