OFFSET
0,2
COMMENTS
Related to the Mathieu group M_24, see references.
Coefficients of the mock modular form H_1^(2). - N. J. A. Sloane, Mar 21 2015
REFERENCES
Miranda C. N. Cheng, John F. R. Duncan and Jeffrey A Harvey, Umbral moonshine and the Niemeier lattices, Research in the Mathematical Sciences, 2014, 1:3; http://www.resmathsci.com/content/1/1/3
Eguchi, T., Ooguri, H., Taormina, A., Yang, S. K., Superconformal algebras and string compactification on manifolds with SU(N) holonomy. Nucl. Phys. B315, 193 (1989). doi:10.1016/0550-3213(89)90454-9
Eguchi, T., Taormina, A., Unitary representations of the N=4 superconformal algebra. Phys. Lett. B. 196(1), 75-81 (1987). doi:10.1016/0370-2693(87)91679-0
Eguchi, T., Taormina, A., Character formulas for the N=4 superconformal algebra. Phys. Lett. B. 200(3), 315-322 (1988). doi:10.1016/0370-2693(88)90778-2
H. Ooguri, Superconformal Symmetry and Geometry of Ricci Flat Kahler Manifolds, Int. J. Mod. Phys. A4 4303, 1989.
LINKS
Miranda C. N. Cheng and John F. R. Duncan, On Rademacher sums, the largest Mathieu group, and the holographic modularity of moonshine (2011)
Miranda C. N. Cheng and John F. R. Duncan, The largest Mathieu group and (mock) automorphic forms (2012)
Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey, Umbral Moonshine, arXiv:1204.2779v3.pdf, Oct 13 2013.
T. Eguchi and K. Hikami, Superconformal algebras and mock theta functions 2. Rademacher expansion for K3 surface, Commun. Number Theor. and Phys. 3, 531-554, 2009. [arXiv:0904.0911].
Tohru Eguchi, Hirosi Ooguri and Yuji Tachikawa, Notes on the K3 surface and the Mathieu group M_24 (2010), arXiv:1004.0956; Exper. Math. 20, 91-96 (2011).
FORMULA
a(n) ~ 2/sqrt(8*n - 1) * exp(2*Pi*sqrt(1/2*(n - 1/8))). This formula gives a good estimate of a(n) even at smaller values of n. [From N-E. Fahssi, Apr 26 2010]
EXAMPLE
G.f. = -1 + 45*x + 231*x^2 + 770*x^3 + 2277*x^4 + 5796*x^5 + 13915*x^6 + ...
G.f. = -1/q + 45*q^7 + 231*q^15 + 770*q^23 + 2277*q^31 + 5796*q^39 + ...
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Apr 19 2010
EXTENSIONS
Added a(0)=-1 and further terms from Cheng et al. Umbral Moonshine paper. - N. J. A. Sloane, Mar 21 2015
STATUS
approved