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A212301
Coefficients of the twisted K3 elliptic genus attached to the conjugacy class 1A in the Mathieu group M_24.
2
-2, 90, 462, 1540, 4554, 11592, 27830, 61686, 131100, 265650, 521136, 988770, 1830248, 3303630, 5844762, 10139734, 17301060, 29051484, 48106430, 78599556, 126894174, 202537080, 319927608, 500376870, 775492564, 1191453912, 1815754710, 2745870180, 4122417420, 6146311620
OFFSET
0,1
COMMENTS
This is the "right" normalization of A169717.
LINKS
Miranda C. N. Cheng and John F. R. Duncan, On Rademacher sums, the largest Mathieu group, and the holographic modularity of moonshine, arXiv:1110.3859 [math.RT], 2011.
Miranda C. N. Cheng and John F. R. Duncan, The largest Mathieu group and (mock) automorphic forms, arXiv:1201.4140 [math.RT], 2012.
Miranda C. N. Cheng, John F. R. Duncan and Jeffrey A. Harvey, Umbral Moonshine, arXiv:1204.2779 [math.RT], 2012-2013. See Table 20.
Tohru Eguchi and Kazuhiro Hikami, Note on Twisted Elliptic Genus of K3 Surface, arXiv:1008.4924 [hep-th], 2010.
Tsuyoshi Miezaki, On the Mathieu mock theta function, Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 2 (2012), 28-30.
FORMULA
a(n) = 2*A169717(n).
PROG
(PARI) E2(q, prec)=1-24*sum(k=1, prec, k*q^k/(1-q^k))
F22(q, prec)=sum(s=1, min(prec-1, sqrt(2*prec)-1/2), my(t=0); forstep(r=s+1, 2*prec\s, 2, t+=(-1)^r*q^(r*s/2)); s*t)
list(lim)=my(q='q+O('q^lim)); Vec((-2*E2(q, lim)+48*F22(q, lim))/eta(q)^3)
CROSSREFS
Sequence in context: A266807 A355574 A076532 * A226339 A157064 A058527
KEYWORD
sign
AUTHOR
Charles R Greathouse IV and John F. R. Duncan, Jun 16 2012
STATUS
approved