A058674 - OEIS

%I #19 Jun 27 2018 11:05:50

%S 1,0,1,3,3,4,7,7,9,15,16,20,29,32,40,55,61,74,99,111,134,170,192,230,

%T 285,323,382,466,530,622,746,848,988,1173,1331,1540,1810,2052,2363,

%U 2752,3114,3568,4129,4663,5318,6118,6895,7834,8963,10078,11410,12993,14579

%N McKay-Thompson series of class 42D for Monster.

%H G. C. Greubel, <a href="/A058674/b058674.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 Expansion of -1 + eta(q^2)*eta(q^6)*eta(q^7)*eta(q^21)/(eta(q)*eta(q^3) *eta(q^14)*eta(q^42)) in powers of q. - _G. C. Greubel_, Jun 24 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 27 2018

%e T42D = 1/q + q + 3*q^2 + 3*q^3 + 4*q^4 + 7*q^5 + 7*q^6 + 9*q^7 + 15*q^8 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A := ((eta[q^2]*eta[q^6]*eta[q^7] *eta[q^21])/(eta[q]*eta[q^3]*eta[q^14]*eta[q^42])); a:=CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 24 2018 *)

%o (PARI) q='q+O('q^50); A = -1 + eta(q^2)*eta(q^6)*eta(q^7)*eta(q^21)/( eta(q)*eta(q^3)*eta(q^14)*eta(q^42))/q; Vec(A) \\ _G. C. Greubel_, Jun 24 2018

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

%K nonn

%O -1,4

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

%E More terms from _Michel Marcus_, Feb 24 2014