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%I #22 Jan 07 2022 08:27:46
%S -1,213,4767,52682,627573,4682412,53313931,341278995,3421674678,
%T 24687536097,214728131688,1291490582217,14602976386348,80718169058895,
%U 691486905294549,5191979939244635,44020035323951778,245857487857551822,2489942402834854279,13633673140696254618
%N 4 times coefficients of the twisted K3 elliptic genus attached to the conjugacy class 7A or 7B (7AB) in the Mathieu group M_24.
%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>, arXiv:1110.3859 [math.RT], 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>, arXiv:1201.4140 [math.RT], 2012.
%H 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.
%o (PARI) F22(q, prec)={
%o sum(s=1,min(prec-1,sqrt(2*prec)-1/2),
%o my(t=0);
%o forstep(r=s+1,2*prec\s,2,
%o t+=(-1)^r*q^(r*s/2)
%o );
%o s*t
%o )
%o };
%o list(n)={
%o my(q='q+O('q^(n+1)),e=eta(q),f=F22(q,n),ser);
%o ser=(6*sum(k=1, n, k*q^k/(1-q^k))+6*f-7*q*log(eta(7*q)/e)'-1/4)/e^3;
%o Vec(4*ser)
%o };
%Y Other conjugacy classes: A212301-A212320.
%K sign
%O 1,2
%A _Charles R Greathouse IV_ and John F. R. Duncan, Aug 02 2012
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