A058684 - OEIS

%I #19 Jun 26 2018 08:43:08

%S 1,0,2,1,3,4,5,6,7,11,15,17,22,24,34,40,48,56,69,84,104,118,144,164,

%T 200,234,273,318,372,436,511,582,681,775,906,1036,1192,1362,1562,1784,

%U 2046,2315,2647,2988,3409,3860,4371,4936,5573,6288,7104,7967,8979,10052

%N McKay-Thompson series of class 45A for Monster.

%H G. C. Greubel, <a href="/A058684/b058684.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 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F Expansion of -1 + (eta(q^3)*eta(q^15))^2/(eta(q)*eta(q^5)*eta(q^9)* eta(q^45)) in powers of q. - _G. C. Greubel_, Jun 19 2018

%F a(n) ~ exp(4*Pi*sqrt(n/5)/3) / (5^(1/4) * sqrt(6) * n^(3/4)). - _Vaclav Kotesovec_, Jun 26 2018

%e T45A = 1/q + 2*q + q^2 + 3*q^3 + 4*q^4 + 5*q^5 + 6*q^6 + 7*q^7 + 11*q^8 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^3]*eta[q^15])^2/(eta[q] *eta[q^5]*eta[q^9]*eta[q^45]); a:= CoefficientList[Series[-1 + e45A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 19 2018 *)

%o (PARI) q='q+O('q^50); A = -1 + (eta(q^3)*eta(q^15))^2/(eta(q)*eta(q^5) *eta(q^9)*eta(q^45))/q; Vec(A) \\ _G. C. Greubel_, Jun 19 2018

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

%Y Cf. A226054 (same sequence except for n=0).

%K nonn

%O -1,3

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

%E More terms from _Michel Marcus_, Feb 18 2014