A188569 Degree of the n-th partition class polynomial Hpart_n(x).

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

Offset: 1

Author

Omar E. Pol, Feb 21 2013

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A183007, A183010, A183011, A183054, A187218.

Extensions

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