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%I #27 Jul 20 2015 22:46:46
%S -1,45,231,770,2277,5796,13915,30843,65550,132825,260568,494385,
%T 915124,1651815,2922381,5069867,8650530,14525742,24053215,39299778,
%U 63447087,101268540,159963804,250188435,387746282,595726956,907877355,1372935090,2061208710,3073155810,4552039296,6700526910
%N 1A coefficients in an expansion of the elliptic genus of the K3 surface.
%C Related to the Mathieu group M_24, see references.
%C Coefficients of the mock modular form H_1^(2). - _N. J. A. Sloane_, Mar 21 2015
%D 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
%D 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
%D 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
%D 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
%D H. Ooguri, Superconformal Symmetry and Geometry of Ricci Flat Kahler Manifolds, Int. J. Mod. Phys. A4 4303, 1989.
%H Miranda C. N. Cheng and John F. R. Duncan, <a href="http://arxiv.org/abs/1110.3859">On Rademacher sums, the largest Mathieu group, and the holographic modularity of moonshine</a> (2011)
%H Miranda C. N. Cheng and John F. R. Duncan, <a href="http://arxiv.org/abs/1201.4140">The largest Mathieu group and (mock) automorphic forms</a> (2012)
%H Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey, <a href="http://arxiv.org/abs/1204.2779">Umbral Moonshine</a>, arXiv:1204.2779v3.pdf, Oct 13 2013.
%H T. Eguchi and K. Hikami, <a href="http://arxiv.org/abs/0904.0911">Superconformal algebras and mock theta functions 2. Rademacher expansion for K3 surface</a>, Commun. Number Theor. and Phys. 3, 531-554, 2009. [arXiv:0904.0911].
%H Tohru Eguchi, Hirosi Ooguri and Yuji Tachikawa, <a href="http://arxiv.org/abs/1004.0956">Notes on the K3 surface and the Mathieu group M_24</a> (2010), arXiv:1004.0956; Exper. Math. 20, 91-96 (2011).
%F 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]
%e G.f. = -1 + 45*x + 231*x^2 + 770*x^3 + 2277*x^4 + 5796*x^5 + 13915*x^6 + ...
%e G.f. = -1/q + 45*q^7 + 231*q^15 + 770*q^23 + 2277*q^31 + 5796*q^39 + ...
%Y Equals A212301/2.
%K sign
%O 0,2
%A _N. J. A. Sloane_, Apr 19 2010
%E Added a(0)=-1 and further terms from Cheng et al. Umbral Moonshine paper. - _N. J. A. Sloane_, Mar 21 2015
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