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A321309
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Coefficients of the power series expansion at p=1 of the growth rate C(p) of the length of the longest increasing path in an Erdös-Rényi graph with edge probability p.
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4
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1, 1, 1, 3, 7, 15, 29, 54, 102, 197, 375, 687, 1226, 2182, 3885, 6828, 11767, 19971, 33519, 55525, 90293, 143350, 221149, 329472, 467362, 611441, 683794, 487644, -425932, -3026915, -9327152, -23364105, -53026834, -113415526, -232986460, -464621237, -905199293
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OFFSET
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0,4
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COMMENTS
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The entries are known to be integers, they were conjectured to be nonnegative and increasing starting from index 2. The radius of convergence of the generating function is at least (sqrt(2)-1)/2 and at most 1.
C(p) is also the speed of the front of the infinite-bin model with moves following a geometric distribution of parameter p.
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LINKS
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EXAMPLE
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C(1+x) = 1 + x + x^2 + 3x^3 + 7x^4 + 15x^5 + ...
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CROSSREFS
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KEYWORD
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sign,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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