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McKay-Thompson series of class 14A for Monster.
2

%I #18 Jun 18 2018 12:29:00

%S 1,0,11,20,57,92,207,312,623,932,1674,2464,4162,6024,9595,13748,21126,

%T 29820,44449,62004,90191,124288,177135,241632,338508,457272,631031,

%U 845008,1150752,1528380,2057700,2712192,3614217,4730148,6245541,8119672

%N McKay-Thompson series of class 14A for Monster.

%H G. C. Greubel, <a href="/A058497/b058497.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) ~ exp(2*Pi*sqrt(2*n/7)) / (2^(3/4) * 7^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 07 2017

%F Expansion of A - 4 + 1/A, where A = (eta(q^2)*eta(q^7)/(eta(q)*eta(q^14) ))^4, in powers of q. - _G. C. Greubel_, Jun 18 2018

%e T14A = 1/q + 11*q + 20*q^2 + 57*q^3 + 92*q^4 + 207*q^5 + 312*q^6 + 623*q^7 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; e14C := (eta[q^2]*eta[q^7]/(eta[q] *eta[q^14]))^4; a:= CoefficientList[Series[-4 + e14C + 1/e14C, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 18 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^7)/(eta(q)*eta(q^14) ))^4/q; Vec(A - 4 + 1/A) \\ _G. C. Greubel_, Jun 18 2018

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

%Y Cf. A134782 (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 19 2014