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A367056
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G.f. satisfies A(x) = 1 + x*A(x)^2 + x^3*A(x).
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1
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1, 1, 2, 6, 17, 52, 168, 561, 1922, 6719, 23871, 85938, 312823, 1149421, 4257460, 15880036, 59594517, 224856450, 852491806, 3245959002, 12407332166, 47592364107, 183139542306, 706794663136, 2735053815771, 10609811267757, 41251228784198
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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.: A(x) = 2 / (1-x^3+sqrt((1-x^3)^2-4*x)).
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k+1,k) * binomial(2*n-5*k,n-3*k)/(n-2*k+1).
D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(-2*n+7)*a(n-3) +(n-8)*a(n-6)=0. - R. J. Mathar, Dec 04 2023
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MAPLE
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add(binomial(n-2*k+1, k) * binomial(2*n-5*k, n-3*k)/(n-2*k+1), k=0..floor(n/3)) ;
end proc:
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PROG
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(PARI) a(n) = sum(k=0, n\3, binomial(n-2*k+1, k)*binomial(2*n-5*k, n-3*k)/(n-2*k+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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