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A045890
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Catafusenes (see reference for precise definition).
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1
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1, 3, 12, 49, 204, 864, 3714, 16170, 71178, 316303, 1417248, 6396273, 29051856, 132700725, 609200640, 2809373915, 13008512040, 60457182345, 281919911460, 1318666411635, 6185356518660, 29088241615910, 137121834221346, 647821223533044, 3066862717614234, 14546629647573969
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1 - x - sqrt(1-6*x+5*x^2))^3/(8*x^3). - Emeric Deutsch, Mar 13 2004
a(n) = (3/n)*Sum_{j=1..n} binomial(n, j)*binomial(2j+2, j-1) for n >= 1. - Emeric Deutsch, Mar 25 2004
Recurrence: (n+2)*(n+3)*a(n) = 2*(n+2)*(3*n+4)*a(n-1) - 5*(n-2)*(n+3)*a(n-2). - Vaclav Kotesovec, Oct 08 2012
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MAPLE
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a := n->(3/n)*sum(binomial(n, j)*binomial(2*j+2, j-1), j=1..n): 1, seq(a(n), n=1..22);
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MATHEMATICA
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a[n_] := 3*(Hypergeometric2F1[5/2, 1-n, 5, -4] + (n-1)*Hypergeometric2F1[7/2, 2-n, 6, -4]); a[0]=1; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jun 13 2012, after Emeric Deutsch *)
CoefficientList[Series[(1-x-Sqrt[1-6x+5x^2])^3/(8x^3), {x, 0, 30}], x] (* Harvey P. Dale, Feb 07 2015 *)
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PROG
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(PARI) x='x+O('x^66); Vec((1-x-sqrt(1-6*x+5*x^2))^3/(8*x^3)) \\ Joerg Arndt, May 04 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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