A058563 - OEIS

%I #22 Jun 18 2018 14:11:12

%S 1,0,6,6,15,30,41,66,111,146,222,336,463,642,942,1238,1698,2334,3090,

%T 4098,5514,7136,9336,12216,15673,20142,26013,32880,41820,53070,66609,

%U 83568,105039,130482,162321,201708,248802,306642,377955,462596,566223,692064

%N McKay-Thompson series of class 21A for Monster.

%H G. C. Greubel, <a href="/A058563/b058563.txt">Table of n, a(n) for n = -1..1000</a>

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

%H David A. Madore, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=1602206&amp;messageID=5836094">Coefficients of Moonshine (McKay-Thompson) series</a>, The Math Forum

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

%F a(n) ~ exp(4*Pi*sqrt(n/21)) / (sqrt(2) * 21^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, May 30 2018

%F Expansion of A + 1 + 7/A, where A = eta(q)*eta(q^3)/(eta(q^7)*eta(q^21)), in powers of q. - _G. C. Greubel_, Jun 18 2018

%e T21A = 1/q + 6*q + 6*q^2 + 15*q^3 + 30*q^4 + 41*q^5 + 66*q^6 + 111*q^7 + ...

%t CoefficientList[Series[((QPochhammer[x^3]^2 * QPochhammer[x^7]^2 - x*QPochhammer[x]^2 * QPochhammer[x^21]^2) / (QPochhammer[x] * QPochhammer[x^3] * QPochhammer[x^7] * QPochhammer[x^21]))^2, {x, 0, 100}], x] (* _Vaclav Kotesovec_, May 30 2018 *)

%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= eta[q]*eta[q^3]/(eta[q^7] *eta[q^21]); a:= CoefficientList[Series[1 + A + 7/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 18 2018 *)

%o (PARI) q='q+O('q^50); A = eta(q)*eta(q^3)/(q*eta(q^7)*eta(q^21)); Vec(A + 1 + 7/A) \\ _G. C. Greubel_, Jun 18 2018

%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

%K nonn

%O -1,3

%A _N. J. A. Sloane_, Nov 27 2000

%E More terms from _Michel Marcus_, Feb 20 2014