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A188569
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Degree of the n-th partition class polynomial Hpart_n(x).
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6
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3, 5, 7, 8, 10, 10, 11, 13, 14, 15, 13, 14, 19, 18, 19, 17, 16, 21, 20, 25, 21, 18, 26, 21, 25, 22, 23, 30, 24, 31, 21, 22, 32, 30, 33, 21, 29, 31, 28, 36, 27, 30, 35, 36, 34, 23, 27, 41, 35, 38, 35, 26, 40, 36, 45, 34, 25, 44, 34, 39, 32, 37, 49, 38, 51, 33
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OFFSET
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1,1
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COMMENTS
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a(n) is the degree of the n-th partition class polynomial whose trace is the numerator of the finite algebraic formula for the number of partitions of n. The formula for the partition function is p(n) = Tr(n)/(24n - 1). See theorem 1.1 in the Bruinier-Ono paper. The traces are in A183011. See also Sutherland's table of Hpart_n(x) in the Links section.
First differs from A183054 at a(24). It appears that this coincides with A183054 in a large number of terms.
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LINKS
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EXAMPLE
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In the Bruinier-Ono paper, chapter 5 "Examples", the first "partition polynomial" is H_1(x) = x^3 - 23*x^2 + (3592/23)*x - 419, which has degree 3, so a(1) = 3.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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This sequence arises from the original definition of A183054 (Jul 14 2011) which was changed.
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STATUS
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approved
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