|
%I #14 Jun 19 2018 12:31:43
%S 1,-3,-1,-3,-2,-9,2,-9,-1,-24,0,-27,5,-51,-3,-60,-4,-108,6,-129,-3,
%T -210,-4,-252,12,-393,-8,-474,-10,-702,16,-852,-9,-1224,-8,-1485,29,
%U -2070,-17,-2511,-22,-3429,38,-4155,-20,-5556,-20,-6723,61,-8856,-36,-10695,-44,-13878,80,-16722,-43
%N McKay-Thompson series of class 24f for Monster.
%H G. C. Greubel, <a href="/A058589/b058589.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 A - 3*q/A, where A = q^(1/2)*(eta(q^2)*eta(q^4))/(eta(q^6) *eta(q^12)), in powers of q. - _G. C. Greubel_, Jun 18 2018
%e T24f = 1/q - 3*q - q^3 - 3*q^5 - 2*q^7 - 9*q^9 + 2*q^11 - 9*q^13 - q^15 - ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^4])/( eta[q^6]*eta[q^12]); a:= CoefficientList[Series[A - 3*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 18 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^4))/(eta(q^6) *eta(q^12)); Vec(A - 3*q/A) \\ _G. C. Greubel_, Jun 18 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 18 2018
|
