

A220481


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


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
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OFFSET

0,2


COMMENTS

Observation: first 13 terms coincide with all terms mentioned in a table of special mock Jacobi forms. See the DabholkarMurthyZagier 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 BruinierOno formula for the number of partitions of n, if n >= 1 (see theorem 1.1 in the BruinierOno 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 halfintegral weight harmonic weak Maass forms
Atish Dabholkar, Sameer Murthy, Don Zagier, Quantum Black Holes, Wall Crossing, and Mock Modular Forms, arXiv:1208.4074 [hepth], 20122014, p. 46, 130.
F. G. Garvan, Congruences for Andrews' sptfunction modulo 32760 and extension of Atkin's Hecketype 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 sptfunction, PNAS January 11, 2011 108 (2) 473476.


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



