A058616 - OEIS

%I #20 Jun 28 2018 03:44:58

%S 1,2,3,6,9,12,18,26,34,48,66,86,115,152,196,252,324,410,518,652,815,

%T 1016,1260,1556,1914,2344,2860,3482,4222,5104,6160,7408,8883,10634,

%U 12694,15112,17962,21300,25198,29764,35091,41284,48495,56870,66567,77800,90790,105780,123070,142988

%N McKay-Thompson series of class 30E for Monster.

%H G. C. Greubel, <a href="/A058616/b058616.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 q^(1/3)*(eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^2 in powers of q. - _G. C. Greubel_, Jun 23 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018

%e T30E = 1/q + 2*q^2 + 3*q^5 + 6*q^8 + 9*q^11 + 12*q^14 + 18*q^17 + 26*q^20 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/3)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 23 2018 *)

%o (PARI) q='q+O('q^50); Vec((eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^2) \\ _G. C. Greubel_, Jun 23 2018

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

%K nonn

%O -1,2

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

%E Terms a(8) onward added by _G. C. Greubel_, Jun 23 2018