A112209 - OEIS

%I #17 Jun 20 2018 06:55:35

%S 1,1,0,1,1,2,2,1,3,3,3,3,4,5,5,7,8,8,9,10,13,15,14,17,20,23,24,26,31,

%T 34,38,41,46,52,55,62,70,75,82,90,103,112,118,131,145,161,172,185,208,

%U 225,244,265,288,316,339,370,404,435,469,507,557,601,640,696,755,818

%N McKay-Thompson series of class 80a for the Monster group.

%H G. C. Greubel, <a href="/A112209/b112209.txt">Table of n, a(n) for n = 0..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>, Comm. 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 a(n) ~ exp(Pi*sqrt(n/5)) / (2^(3/2) * 5^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 30 2017

%F Expansion of q^(1/4)*(eta(q^2)*eta(q^10))^2/( eta(q)*eta(q^4)*eta(q^5) *eta(q^20)) in powers of q. - _G. C. Greubel_, Jun 20 2018

%e T80a = 1/q +q^3 +q^11 +q^15 +2*q^19 +2*q^23 +q^27 +3*q^31 +...

%t nmax = 70; CoefficientList[Series[Product[(1 + x^(2*k-1))/((1 + x^(10*k))*(1 - x^(10*k-5))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 30 2017 *)

%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/4)*(eta[q^2]*eta[q^10])^2/( eta[q]*eta[q^4]*eta[q^5]*eta[q^20]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 70}] (* _G. C. Greubel_, Jun 20 2018 *)

%o (PARI) q='q+O('q^70); Vec((eta(q^2)*eta(q^10))^2/( eta(q)*eta(q^4) *eta(q^5)*eta(q^20))) \\ _G. C. Greubel_, Jun 20 2018

%Y Cf. A112182.

%K nonn

%O 0,6

%A _Michael Somos_, Aug 28 2005