A222032 -id:A222032 - cp's OEIS frontend

A220515 Numbers n such that A183054(n) is not equal to A188569(n).

24, 47, 49, 74, 96, 99, 116, 124, 145, 149, 162, 174, 194, 199, 224, 237, 243, 249, 274, 277, 292, 299, 324, 331, 341, 346, 349, 358, 374, 390, 399, 424, 439, 449, 474, 479, 488, 499, 500, 507, 524, 537, 549, 566, 574, 586, 599, 600, 624, 635

Offset: 1

Omar E. Pol, Feb 27 2013

nonn

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. For more information see A222031.

			First three terms are 24, 47, 49 because first 50 terms of A183054 coincide with first 50 terms of A188569 except for the indices 24, 47, 49 as shown below:
(A183054(24) = 3) < (A188569(24) = 21).
(A183054(47) = 3) < (A188569(47) = 27).
(A183054(49) = 5) < (A188569(49) = 35).
Observation:
A183054(24) = A188569(24)/7 = 3.
A183054(47) = A188569(47)/9 = 3.
A183054(49) = A188569(49)/7 = 5.

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

Cf. A000041, A183010, A183011, A183054, A188569, A222031, A222032.

a(4)-a(50) from Giovanni Resta, Mar 04 2013

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.

Original entry on oeis.org

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

Omar E. Pol, Mar 04 2013

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.

			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;
...

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

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.

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

cp's OEIS Frontend

A220515 Numbers n such that A183054(n) is not equal to A188569(n).

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