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A180473
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Expansion of o.g.f. x*s(x)/(1-x*s(x)-x^2*s(x)^2), where s(x) is the o.g.f. of the little Schroeder numbers (A001003).
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1
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1, 2, 7, 27, 114, 509, 2365, 11318, 55411, 276231, 1397430, 7156089, 37023225, 193229466, 1016141199, 5378940051, 28638955098, 153267403397, 824014568581, 4448456379134, 24104579252971, 131055735586767, 714741620026542, 3908997981612017, 21434123083817329
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} (k/(2^k*n))*(Sum_{j=0..n-k} binomial(n,j)*2^(n-j)*(-1)^j*binomial(2*n-k-j-1, n-1))*Fibonacci(k).
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PROG
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(Maxima) a(n):=sum(k/(2^k*n)*sum(binomial(n, j)*2^(n-j)*(-1)^j*binomial(2*n-k-j-1, n-1), j, 0, n-k)*fib(k), k, 1, n);
(PARI) seq(n)={my(p=x*(1+x-sqrt(1 - 6*x + x^2 + O(x*x^n)))/(4*x)); Vec(p/(1 - p - p^2))} \\ Andrew Howroyd, Apr 17 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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