A212312 4 times coefficients of the twisted K3 elliptic genus attached to the conjugacy class 7A or 7B (7AB) in the Mathieu group M_24.

-1, 213, 4767, 52682, 627573, 4682412, 53313931, 341278995, 3421674678, 24687536097, 214728131688, 1291490582217, 14602976386348, 80718169058895, 691486905294549, 5191979939244635, 44020035323951778, 245857487857551822, 2489942402834854279, 13633673140696254618

Offset

1,2

Links

Table of n, a(n) for n=1..20.

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.

Tohru Eguchi and Kazuhiro Hikami, Note on Twisted Elliptic Genus of K3 Surface, arXiv:1008.4924 [hep-th], 2010.

Prog

(PARI) 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(n)={
    my(q='q+O('q^(n+1)), e=eta(q), f=F22(q, n), ser);
    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;
    Vec(4*ser)
};

Crossrefs

Other conjugacy classes: A212301-A212320.

Sequence in context: A302256 A092127 A082967 * A201342 A092796 A280898

Adjacent sequences: A212309 A212310 A212311 * A212313 A212314 A212315

Keyword

sign

Author

Charles R Greathouse IV and John F. R. Duncan, Aug 02 2012

Status

approved