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

Author

Omar E. Pol, Mar 04 2013

Keywords

• sign
• frac
• tabf

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.

Examples

			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;
...
		

Links

• 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

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.

Formula

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