OFFSET
0,2
COMMENTS
Observation: first 13 terms coincide with all terms mentioned in a table of special mock Jacobi forms. See the Dabholkar-Murthy-Zagier paper, appendix A.1, table of Q_M (weight 2 case), M = 6, C_M = 12. See also the table in page 46.
Question: do all terms coincide?
The formula 12spt(n) + (24n - 1)p(n) is mentioned in several papers (see Ono's paper, see also Garvan's papers and Garvan's slides in link section).
Also a(n) = 12spt + Tr(n), where Tr(n) is the numerator of the Bruinier-Ono formula for the number of partitions of n, if n >= 1 (see theorem 1.1 in the Bruinier-Ono paper). Tr(n) is also the trace of the partition class polynomial Hpart_n(x). For more information see A183011.
LINKS
J. H. Bruinier and K. Ono, Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
Atish Dabholkar, Sameer Murthy, Don Zagier, Quantum Black Holes, Wall Crossing, and Mock Modular Forms, arXiv:1208.4074 [hep-th], 2012-2014, p. 46, 130.
F. G. Garvan, Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences, arXiv:1011.1957 [math.NT], 2010, see (1.5), (2.12).
F. G. Garvan, The smallest parts partition function, slides, 2012
Ken Ono, Congruences for the Andrews spt-function, PNAS January 11, 2011 108 (2) 473-476.
FORMULA
CROSSREFS
KEYWORD
sign
AUTHOR
Omar E. Pol, Jan 14 2013
STATUS
approved