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A247102
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G.f.: (6*x+2)/(sqrt(-3*x^2-6*x+1)*(4*x^2+4*x))-(2*x+1)/(2*x^2+2*x).
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0
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2, 10, 53, 298, 1727, 10207, 61154, 370090, 2256983, 13848085, 85387040, 528646015, 3284180720, 20462505850, 127816245053, 800143927210, 5018683475087, 31532297088781, 198419993271440, 1250291989478773, 7888160383113014
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = sum(i=0..n+1, binomial(2*n-i+1,n-i+1)*sum(j=0..n+1, binomial(j,-j+i)* binomial(n+1,j)).
a(n) ~ sqrt(3) * (3+2*sqrt(3))^(n+1) / (2*sqrt(2*Pi*n)). - Vaclav Kotesovec, Nov 23 2014
Conjecture D-finite with recurrence: (n+1)*a(n) +(-2*n-5)*a(n-1) +3*(-8*n+7)*a(n-2) +15*(-2*n+3)*a(n-3) +9*(-n+2)*a(n-4)=0. - R. J. Mathar, Jan 25 2020
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MATHEMATICA
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CoefficientList[Series[(6 x + 2) / (Sqrt[-3 x^2 - 6 x + 1] (4 x^2 + 4 x)) - (2 x + 1) / (2 x^2 + 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 22 2014 *)
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PROG
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(Maxima)
a(n):=sum(binomial(2*n-i+1, n-i+1)*sum(binomial(j, -j+i)*binomial(n+1, j), j, 0, n+1), i, 0, n+1);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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