cp's OEIS Frontend

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

%I A188569 #51 Aug 11 2014 22:45:46
%S A188569 3,5,7,8,10,10,11,13,14,15,13,14,19,18,19,17,16,21,20,25,21,18,26,21,
%T A188569 25,22,23,30,24,31,21,22,32,30,33,21,29,31,28,36,27,30,35,36,34,23,27,
%U A188569 41,35,38,35,26,40,36,45,34,25,44,34,39,32,37,49,38,51,33
%N A188569 Degree of the n-th partition class polynomial Hpart_n(x).
%C A188569 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.
%C A188569 First differs from A183054 at a(24). It appears that this coincides with A183054 in a large number of terms.
%H A188569 Giovanni Resta, <a href="/A188569/b188569.txt">Table of n, a(n) for n = 1..750. Data from A. V. Sutherland's website</a>
%H A188569 J. H. Bruinier and K. Ono, <a href="http://www.aimath.org/news/partition/brunier-ono.pdf">Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms</a>
%H A188569 J. H. Bruinier, K. Ono, A. V. Sutherland, <a href="http://arxiv.org/abs/1301.5672">Class polynomials for nonholomorphic modular functions</a>
%H A188569 A. V. Sutherland, <a href="http://math.mit.edu/~drew/Pfiles">Partition class polynomials</a>, Hpart_n(x), n = 1..770
%e A188569 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.
%Y A188569 Cf. A183007, A183010, A183011, A183054, A187218.
%K A188569 nonn
%O A188569 1,1
%A A188569 _Omar E. Pol_, Feb 21 2013
%E A188569 This sequence arises from the original definition of A183054 (Jul 14 2011) which was changed.