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A220481
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a(n) = 12spt(n) + (24n - 1)p(n), with a(0) = -1.
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1
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-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
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0,2
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COMMENTS
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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.
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LINKS
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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.
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FORMULA
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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.
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CROSSREFS
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Cf. A000041, A092269, A183010, A183011, A211609, A220908.
Sequence in context: A225930 A209370 A219717 * A144492 A192926 A120398
Adjacent sequences: A220478 A220479 A220480 * A220482 A220483 A220484
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KEYWORD
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sign
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AUTHOR
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Omar E. Pol, Jan 14 2013
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STATUS
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approved
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