A212301 Coefficients of the twisted K3 elliptic genus attached to the conjugacy class 1A in the Mathieu group M_24.

-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

Table of n, a(n) for n=0..29.

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

Cf. A169717, A212312.

Sequence in context: A266807 A355574 A076532 * A226339 A157064 A058527

Adjacent sequences: A212298 A212299 A212300 * A212302 A212303 A212304

Keyword

sign

Author

Charles R Greathouse IV and John F. R. Duncan, Jun 16 2012

Status

approved