cp's OEIS Frontend

A220481 a(n) = 12spt(n) + (24n - 1)p(n), with a(0) = -1.

%I A220481 #51 Aug 09 2020 07:25:18
%S A220481 -1,35,130,273,595,1001,1885,2925,4886,7410,11466,16660,24955,35191,
%T A220481 50505,70252,98085,133455,182819,244790,329121,435420,576030,752609,
%U A220481 984165,1271998,1643460,2105450,2693522,3420235,4338552,5466370,6878235,8607417
%N A220481 a(n) = 12spt(n) + (24n - 1)p(n), with a(0) = -1.
%C A220481 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.
%C A220481 Question: do all terms coincide?
%C A220481 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).
%C A220481 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.
%H A220481 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 A220481 Atish Dabholkar, Sameer Murthy, Don Zagier, <a href="http://arxiv.org/abs/1208.4074">Quantum Black Holes, Wall Crossing, and Mock Modular Forms</a>, arXiv:1208.4074 [hep-th], 2012-2014, p. 46, 130.
%H A220481 F. G. Garvan, <a href="http://arxiv.org/abs/1011.1957">Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences</a>, arXiv:1011.1957 [math.NT], 2010, see (1.5), (2.12).
%H A220481 F. G. Garvan, <a href="https://carma.newcastle.edu.au/meetings/alfcon/pdfs/Frank_Garvan-alfcon.pdf">The smallest parts partition function</a>, slides, 2012
%H A220481 Ken Ono, <a href="http://dx.doi.org/10.1073/pnas.1015339107">Congruences for the Andrews spt-function</a>, PNAS January 11, 2011 108 (2) 473-476.
%F A220481 a(n) = 12spt(n) + Tr(n) = 12(3spt(n) + N_2(n)) - p(n), n >= 1.
%F A220481 a(n) = A211609(n) + A183011(n) = 12*A092269(n) + A183011(n) = 12*A092269(n) + A183010(n)*A000041(n) = 12(3*A092269(n) + A220908(n)) - A000041(n), n >= 1.
%Y A220481 Cf. A000041, A092269, A183010, A183011, A211609, A220908.
%K A220481 sign
%O A220481 0,2
%A A220481 _Omar E. Pol_, Jan 14 2013