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A277969
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a(n) = Sum_{k=0..n} binomial(n-3,n-k)*Catalan(k).
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1
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1, -1, 2, 5, 19, 75, 305, 1270, 5390, 23236, 101480, 448085, 1997115, 8973255, 40602093, 184853055, 846206025, 3892585325, 17984308775, 83417287855, 388297304825, 1813341109825, 8493372326675, 39889629750600, 187812852106636
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: ((1-x)^3*(1-sqrt((5*x-1)/(x-1))))/(2*x).
(5*n-10)*a(n)-(7+6*n)*a(n+1)+(n+3)*a(n+2)=0 for n >= 2. - Robert Israel, Nov 21 2016
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MAPLE
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f:= gfun:-rectoproc({(5*n-10)*a(n)+(-7-6*n)*a(n+1)+(n+3)*a(n+2), a(0) = 1, a(1) = -1, a(2) = 2, a(3) = 5}, a(n), remember):
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MATHEMATICA
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CoefficientList[Series[((1 - x)^3 (1 - Sqrt[(5 x - 1) / (x - 1)])) / (2 x), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 07 2016 *)
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PROG
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(Maxima)
a(n):=sum((binomial(2*k, k)*binomial(n-3, n-k))/(k+1), k, 0, n);
(PARI) x='x+O('x^50); Vec(((1-x)^3*(1-sqrt((5*x-1)/(x-1))))/(2*x)) \\ G. C. Greubel, Apr 09 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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