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McKay-Thompson series of class 36c for Monster.
1

%I #14 Jun 23 2018 14:17:11

%S 1,2,0,-1,2,0,0,2,0,-2,6,0,2,6,0,-1,8,0,2,14,0,-2,16,0,3,20,0,-4,32,0,

%T 4,38,0,-4,46,0,7,66,0,-7,78,0,6,96,0,-10,130,0,11,154,0,-11,186,0,14,

%U 244,0,-16,288,0,17,346,0,-21,440,0,22,518,0,-24,618,0,32,768,0,-34,902,0,34,1068

%N McKay-Thompson series of class 36c for Monster.

%H G. C. Greubel, <a href="/A058650/b058650.txt">Table of n, a(n) for n = -1..2500</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 Expansion of A + 2*q/A, where A = q^(1/2)*(eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))), in powers of q. - _G. C. Greubel_, Jun 23 2018

%e T36c = 1/q + 2*q - q^5 + 2*q^7 + 2*q^13 - 2*q^17 + 6*q^19 + 2*q^23 + 6*q^25 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^9]/(eta[q^6]*eta[q^18])); a:= CoefficientList[Series[A + 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 23 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))); Vec(A + 2*q/A) \\ _G. C. Greubel_, Jun 23 2018

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

%K sign

%O -1,2

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

%E Terms a(12) onward added by _G. C. Greubel_, Jun 23 2018