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

-1, 35, 130, 273, 595, 1001, 1885, 2925, 4886, 7410, 11466, 16660, 24955, 35191, 50505, 70252, 98085, 133455, 182819, 244790, 329121, 435420, 576030, 752609, 984165, 1271998, 1643460, 2105450, 2693522, 3420235, 4338552, 5466370, 6878235, 8607417

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

Table of n, a(n) for n=0..33.

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

a(n) = 12spt(n) + Tr(n) = 12(3spt(n) + N_2(n)) - p(n), n >= 1.

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.

Crossrefs

Cf. A000041, A092269, A183010, A183011, A211609, A220908.

Sequence in context: A225930 A209370 A219717 * A144492 A192926 A120398

Adjacent sequences: A220478 A220479 A220480 * A220482 A220483 A220484

Keyword

sign

Author

Omar E. Pol, Jan 14 2013

Status

approved