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A019450
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Conjectured formula for irreducible 5-fold Euler sums of weight 2n+13.
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1
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1, 2, 5, 9, 15, 23, 36, 50, 71, 96, 127, 165, 213, 266, 333, 409, 498, 600, 720, 851, 1005, 1176, 1368, 1582, 1824, 2085, 2381, 2703, 3057, 3444, 3871, 4328, 4833, 5376, 5964, 6598, 7287, 8018, 8813, 9660, 10567, 11536, 12576, 13673, 14852, 16099, 17424, 18828
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OFFSET
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1,2
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COMMENTS
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The conjectured formula has been verified by David Broadhurst up to a(12) = 165.
See D. J. Broadhurst link for definition and additional formulas. Perhaps this sequence should rather have offset 0? - Andrew Howroyd, Jan 01 2020
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REFERENCES
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D. J. Broadhurst, Conjectural enumeration of irreducible MZV's: terashuffle tests at depth 4, up to weight 36, preprint, Oct 13 1996.
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LINKS
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FORMULA
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G.f.: x*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4)/((1 - x^2)^2*(1 - x^3)^2*(1 - x^5)). - Andrew Howroyd, Jan 01 2020
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PROG
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(PARI) Vec((1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4)/((1 - x^2)^2*(1 - x^3)^2*(1 - x^5)) + O(x^40)) \\ Andrew Howroyd, Jan 01 2020
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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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