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Search: id:A098618
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| 1, 3, 22, 195, 1946, 20790, 232716, 2693691, 31979090, 387243714, 4764470932, 59391201870, 748472730628, 9520446996300, 122067269204760, 1575965219205195, 20470515781159170, 267325017886787850
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OFFSET
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0,2
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COMMENT
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Radius of convergence: r = (sqrt(17)-3)/16; A(r) = sqrt(2+6/sqrt(17)). Recurrence of A007482 is A007482(n) = 3*A007482(n-1) + 2*A007482(n-2). More generally, given {S} such that: S(n) = b*S(n-1) + c*S(n-2), |b|>0, |c|>0, then Sum_{n>=0} S(n)*Catalan(n)*x^n = sqrt( (1-2*b*x - sqrt(1-4*b*x-16*c*x^2))/(2*b^2+8*c) )/x.
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FORMULA
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G.f.: A(x) = sqrt((1-6*x - sqrt(1-12*x-32*x^2))/34 )/x.
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EXAMPLE
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Begins: {1*1, 3*1, 11*2, 39*5, 139*14, 495*42, 1763*132, 6279*429,...}.
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PROGRAM
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(PARI) {a(n)=binomial(2*n, n)/(n+1)*((3+sqrt(17))^(n+1)-(3-sqrt(17))^(n+1))/2^(n+1)/sqrt(17)}
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CROSSREFS
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Cf. A007482, A000108, A098614, A098616, A098619.
Sequence in context: A001393 A046743 A121952 this_sequence A006783 A001409 A079489
Adjacent sequences: A098615 A098616 A098617 this_sequence A098619 A098620 A098621
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 09 2004
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