login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188569 Degree of the n-th 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 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.

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 half-integral 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 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.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 17:07 EDT 2022. Contains 353847 sequences. (Running on oeis4.)