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A289245
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Coefficients of 1/(Sum_{k>=0} [-1 + (k+1)*r](-x)^k), where r = (3 + sqrt(5))/2 = 1 + golden ratio and [ ] = floor.
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1
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1, 4, 10, 25, 64, 162, 408, 1027, 2584, 6500, 16351, 41132, 103468, 260272, 654709, 1646907, 4142758, 10421013, 26213819, 65940258, 165871197, 417245167, 1049570586, 2640170577, 6641288127, 16706006942, 42023574736, 105709331958, 265909383794, 668888915293
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OFFSET
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0,2
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COMMENTS
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Conjecture: the sequence is strictly increasing.
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LINKS
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FORMULA
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G.f.: 1/(Sum_{k>=0} [(-1 + (k+1)*r](-x)^k), where r = (3 + sqrt(5))/2 = 1 + golden ratio and [ ] = floor.
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MATHEMATICA
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CoefficientList[Series[1/Sum[Floor[-1 + (k + 1)*(1 + GoldenRatio)] (-x)^k, {k, 0, 100}], {x, 0, 50}], x]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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