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A276994
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Decimal expansion of the Klarner-Rivest polyomino constant.
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3
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2, 3, 0, 9, 1, 3, 8, 5, 9, 3, 3, 3, 0, 4, 9, 4, 7, 3, 1, 0, 9, 8, 7, 2, 0, 3, 0, 5, 0, 1, 7, 2, 1, 2, 5, 3, 1, 9, 1, 1, 8, 1, 4, 4, 7, 2, 5, 8, 1, 6, 2, 8, 4, 0, 1, 6, 9, 4, 4, 0, 2, 9, 0, 0, 2, 8, 4, 4, 5, 6, 4, 4, 0, 7, 4, 8, 3, 1, 6, 8, 4, 2, 7, 1, 7, 2, 8, 1, 6, 1, 5, 7, 7, 4, 4, 1, 2, 1, 7, 4, 3, 7, 4, 6, 1
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OFFSET
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1,1
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COMMENTS
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Analytic Combinatorics (Flajolet and Sedgewick, 2009, p. 662) has a wrong value of this constant (2.309138593331230...).
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.19 (Klarner's polyomino constant), p. 380.
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LINKS
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FORMULA
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Equals lim n -> infinity A006958(n)^(1/n).
1/A276994 = 0.4330619231293906645846169654189837... is the smallest positive root of the equation Sum_{n>=0} ((-1)^n * z^(n*(n+1)/2) / (Product_{k=1..n} 1-z^k)^2) = 0.
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EXAMPLE
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2.309138593330494731098720305017212531911814472581628401694402900284456440748...
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MATHEMATICA
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1/z/.FindRoot[Sum[(-1)^n * z^(n*(n+1)/2) / QPochhammer[z, z, n]^2, {n, 0, 1000}], {z, 2/5}, WorkingPrecision -> 120]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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