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A098614
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Product of Fibonacci and Catalan numbers: a(n) = A000045(n+1)*A000108(n).
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7
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1, 1, 4, 15, 70, 336, 1716, 9009, 48620, 267410, 1494844, 8465184, 48466796, 280073300, 1631408400, 9568812015, 56466198990, 335002137360, 1997007404700, 11955535480350, 71850862117320, 433322055191220, 2621615826231480
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Radius of convergence: r = (sqrt(5)-1)/8; A(r) = sqrt(2+2/sqrt(5)). 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
| G.f.: A(x) = sqrt( (1-2*x - sqrt(1-4*x-16*x^2))/10 )/x.
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EXAMPLE
| Begins: {1*1, 1*1, 2*2, 3*5, 5*14, 8*42, 13*132, 21*429,...}.
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MATHEMATICA
| With[{nn=30}, Times@@@Thread[{Fibonacci[Range[nn]], CatalanNumber[ Range[ 0, nn-1]]}]] (* From Harvey P. Dale, Nov 14 2011 *)
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PROG
| (PARI) {a(n)=binomial(2*n, n)/(n+1)*((1+sqrt(5))^(n+1)-(1-sqrt(5))^(n+1))/(2^(n+1)*sqrt(5))}
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CROSSREFS
| Cf. A000045, A000108, A098615, A098616, A098618.
Sequence in context: A039625 A020020 A000882 * A027316 A085349 A026992
Adjacent sequences: A098611 A098612 A098613 * A098615 A098616 A098617
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 09 2004
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