

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

Giovanni Resta, Table of n, a(n) for n = 1..750. Data from A. V. Sutherland's website
J. H. Bruinier and K. Ono, Algebraic formulas for the coefficients of halfintegral weight harmonic weak Maass forms
J. H. Bruinier, K. Ono, A. V. Sutherland, Class polynomials for nonholomorphic modular functions
A. V. Sutherland, Partition class polynomials, Hpart_n(x), n = 1..770


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

Cf. A183007, A183010, A183011, A183054, A187218.
Sequence in context: A185011 A175144 A183054 * A274140 A212294 A299495
Adjacent sequences: A188566 A188567 A188568 * A188570 A188571 A188572


KEYWORD

nonn


AUTHOR

Omar E. Pol, Feb 21 2013


EXTENSIONS

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


STATUS

approved



