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A299502
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Expansion of (1 - 6*x + x^2 + 8*x^3 + 16*x^4)^(-1/2).
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2
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1, 3, 13, 59, 277, 1347, 6685, 33675, 171493, 880531, 4550125, 23633627, 123272117, 645247715, 3387538621, 17830213931, 94058445445, 497152260915, 2632288649869, 13958805204603, 74124967884373, 394115410904195, 2097849420888925, 11178238250228427
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OFFSET
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0,2
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COMMENTS
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See A299500 for a family of related polynomials.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} 2^k*binomial(n,k)*hypergeom([-k,k-n,k-n], [1,-n], 2).
D-finite with recurrence: (16*n-32)*a(n-4) + (8*n-12)*a(n-3) + (n-1)*a(n-2) + (3-6*n)*a(n-1) + n*a(n) = 0.
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MAPLE
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a := n -> add(2^k*binomial(n, k)*hypergeom([-k, k-n, k-n], [1, -n], 2), k=0..n):
seq(simplify(a(n)), n=0..28);
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MATHEMATICA
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CoefficientList[Series[(1 - 6x + x^2 + 8x^3 + 16x^4)^(-1/2), {x, 0, 23}], x]
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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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