A222031 Irregular triangle read by rows in which row n gives numerators of the coefficients of the partition class polynomial Hpart_n(x), n >= 1.

1, -23, 3592, -419, 1, -94, 169659, -65838, 1092873176, 145023, 1, -213, 1312544, -723721, 44648582886, 9188934683, 166629520876208, 2791651635293, 1, -475, 9032603, -9455070, 3949512899743, -97215753021, 9776785708507683, -53144327916296, -134884469547631

Offset

1,2

Comments

For an algorithm to compute the partition class polynomial Hpart_n(x) see the Bruinier-Ono-Sutherland paper, 3.3. Algorithm 3, p. 15-19.

Note that the absolute value of T(n,2) is also the trace Tr(n) = A183011(n), the numerator of the finite algebraic formula for the number of partitions of n. The formula is p(n) = Tr(n)/(24*n - 1). See theorem 1.1 in the Bruinier-Ono paper.

Links

Table of n, a(n) for n=1..27.

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), for n = 1..770

Formula

abs(T(n,2))/(24n-1) = A183011(n)/A183010(n) = A000041(n).

Example

For n = 1 the first partition class polynomial Hpart_1(x) is x^3 - 23*x^2 + 3592/23*x - 419, so the numerators of the coefficients are 1, -23, 3592, -419.
Triangle begins:
1, -23, 3592, -419;
1, -94, 169659, -65838, 1092873176, 145023;
1, -213, 1312544, -723721, 44648582886, 9188934683, 166629520876208, 2791651635293;
1, -475, 9032603, -9455070, 3949512899743, -97215753021, 9776785708507683, -53144327916296, -134884469547631;
...

Crossrefs

Row n has length 1 + A188569(n). Absolute values of column 2 give A183011. Columns 3-4: A183007, A187218. For denominators see A222032.

Cf. A000041, A183010, A220515.

Sequence in context: A340330 A290786 A248335 * A233143 A134798 A368137

Adjacent sequences: A222028 A222029 A222030 * A222032 A222033 A222034

Keyword

sign,frac,tabf

Author

Omar E. Pol, Mar 04 2013

Status

approved