cp's OEIS Frontend

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

%I A212301 #18 Jan 07 2022 08:26:20
%S A212301 -2,90,462,1540,4554,11592,27830,61686,131100,265650,521136,988770,
%T A212301 1830248,3303630,5844762,10139734,17301060,29051484,48106430,78599556,
%U A212301 126894174,202537080,319927608,500376870,775492564,1191453912,1815754710,2745870180,4122417420,6146311620
%N A212301 Coefficients of the twisted K3 elliptic genus attached to the conjugacy class 1A in the Mathieu group M_24.
%C A212301 This is the "right" normalization of A169717.
%H A212301 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>, arXiv:1110.3859 [math.RT], 2011.
%H A212301 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>, arXiv:1201.4140 [math.RT], 2012.
%H A212301 Miranda C. N. Cheng, John F. R. Duncan and Jeffrey A. Harvey, <a href="http://arxiv.org/abs/1204.2779">Umbral Moonshine</a>, arXiv:1204.2779 [math.RT], 2012-2013. See Table 20.
%H A212301 Tohru Eguchi and Kazuhiro Hikami, <a href="http://arxiv.org/abs/1008.4924">Note on Twisted Elliptic Genus of K3 Surface</a>, arXiv:1008.4924 [hep-th], 2010.
%H A212301 Tsuyoshi Miezaki, <a href="http://dx.doi.org/10.3792/pjaa.88.28">On the Mathieu mock theta function</a>, Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 2 (2012), 28-30.
%F A212301 a(n) = 2*A169717(n).
%o A212301 (PARI) E2(q,prec)=1-24*sum(k=1,prec,k*q^k/(1-q^k))
%o A212301 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)
%o A212301 list(lim)=my(q='q+O('q^lim));Vec((-2*E2(q,lim)+48*F22(q,lim))/eta(q)^3)
%Y A212301 Cf. A169717, A212312.
%K A212301 sign
%O A212301 0,1
%A A212301 _Charles R Greathouse IV_ and John F. R. Duncan, Jun 16 2012