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McKay-Thompson series of class 27d for Monster.
2

%I #12 Jun 22 2018 15:11:19

%S 1,2,-1,0,3,-2,3,4,0,4,8,-4,5,12,-5,8,16,-6,14,28,-11,14,37,-16,26,50,

%T -17,36,75,-30,46,100,-39,64,129,-48,92,184,-71,108,238,-94,156,308,

%U -110,202,413,-160,253,530,-203,332,670,-248,437,880,-332,528,1107,-424,696,1388,-508,876,1773,-672,1079,2212,-831,1362,2735,-1012,1717,3446,-1288

%N McKay-Thompson series of class 27d for Monster.

%H G. C. Greubel, <a href="/A058604/b058604.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>, 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 (6 + T9b)^(1/3), where T9b = A112146, in powers of q^3. - _G. C. Greubel_, Jun 22 2018

%e T27d = 1/q + 2*q^2 - q^5 + 3*q^11 - 2*q^14 + 3*q^17 + 4*q^20 + 4*q^26 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q*(eta[q^3]/eta[q^9])^4; T9b := A + 9*q^2/A; a:= CoefficientList[Series[(6*q^3 + (T9b /. {q -> q^3}) + O[q]^nmax)^(1/3), {q, 0, 300}], q]; Table[a[[n]], {n, 1, 120}][[1 ;; ;; 3]] (* _G. C. Greubel_, Jun 22 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(8) onward added by _G. C. Greubel_, Jun 22 2018