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McKay-Thompson series of class 22B for Monster.
2

%I #22 Jun 18 2018 14:10:19

%S 1,0,1,-2,4,-4,5,-6,9,-12,13,-18,25,-28,33,-44,54,-64,74,-92,114,-132,

%T 155,-186,224,-260,303,-360,424,-488,565,-662,770,-888,1018,-1180,

%U 1366,-1560,1780,-2048,2345,-2668,3034,-3460,3946,-4468,5052,-5734,6502,-7328,8255,-9320,10512,-11808

%N McKay-Thompson series of class 22B for Monster.

%H G. C. Greubel, <a href="/A058568/b058568.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 a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/11)) / (2*11^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2017

%F Expansion of 2 + (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2 in powers of q. - _G. C. Greubel_, Jun 18 2018

%e T22B = 1/q + q - 2*q^2 + 4*q^3 - 4*q^4 + 5*q^5 - 6*q^6 + 9*q^7 - 12*q^8 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[2 + (eta[q]*eta[q^11]/(eta[q^2]*eta[q^22]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 18 2018 *)

%o (PARI) q='q+O('q^50); A = 2 +(eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2/q; Vec(A) \\ _G. C. Greubel_, Jun 18 2018

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

%Y Cf. A132320 (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 18 2014