A058509 - OEIS

%I #22 Jun 14 2018 03:19:58

%S 1,0,-1,4,-3,-2,11,-6,-11,20,-15,-16,43,-24,-32,76,-48,-58,144,-84,

%T -97,238,-144,-172,398,-234,-279,636,-372,-428,1012,-582,-678,1564,

%U -906,-1028,2389,-1362,-1576,3560,-2046,-2320,5290,-2988,-3407,7700,-4371,-4928

%N McKay-Thompson series of class 15B for Monster.

%H G. C. Greubel, <a href="/A058509/b058509.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 2 + (eta(q)*eta(q^5)/(eta(q^3)*eta(q^15)))^2 in powers of q. - _G. C. Greubel_, Jun 14 2018

%e T15B = 1/q - q + 4*q^2 - 3*q^3 - 2*q^4 + 11*q^5 - 6*q^6 - 11*q^7 + 20*q^8 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; b:= (eta[q]*eta[q^5]/(eta[q^3]* eta[q^15]))^2; a:= CoefficientList[Series[q*(2 + b), {q, 0, 60}], q]; Table[a[[n]], {n,1,50}] (* _G. C. Greubel_, Feb 13 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q)*eta(q^5)/(eta(q^3)*eta(q^15)))^2/q; Vec(2 + A) \\ _G. C. Greubel_, Jun 14 2018

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

%Y Cf. A093067 (same sequence except for n=0).

%K sign

%O -1,4

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

%E More terms from _Michel Marcus_, Feb 19 2014