A045485 - OEIS

%I #23 Jun 28 2018 04:13:15

%S 1,7,78,364,1365,4380,12520,32772,80094,185276,409578,871272,1792754,

%T 3582708,6977100,13277472,24747867,45267324,81389908,144048396,

%U 251265288,432425864,734953116,1234647216,2051576037

%N McKay-Thompson series of class 6B for Monster with a(0) = 7.

%H G. C. Greubel, <a href="/A045485/b045485.txt">Table of n, a(n) for n = -1..1000</a>

%H I. Chen and N. Yui, <a href="http://people.math.sfu.ca/~ichen/pub/chen-yui.pdf">Singular values of Thompson series</a>. In Groups, difference sets and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 1996.

%H J. H. Conway and S. P. Norton, <a href="https://doi.org/10.1112/blms/11.3.308">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%H D. Ford, J. McKay and S. P. Norton, <a href="https://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).

%H J. McKay and H. Strauss, <a href="https://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F Expansion of -5 + (eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^12 in powers of q. - _G. C. Greubel_, Jun 12 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 26 2018

%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-5 + (eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^12), {q, 0, 60}], q];

%t Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 12 2018 *)

%o (PARI) q='q+O('q^30); A=-5+(eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^12/q; Vec(A) \\ _G. C. Greubel_, Jun 12 2018

%Y Cf. A007255.

%K nonn

%O -1,2

%A _N. J. A. Sloane_