

A188569


Degree of the nth partition class polynomial Hpart_n(x).


6



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

1,1


COMMENTS

a(n) is the degree of the nth 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 BruinierOno 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.


LINKS



EXAMPLE

In the BruinierOno 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.


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

This sequence arises from the original definition of A183054 (Jul 14 2011) which was changed.


STATUS

approved



