cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A058489 McKay-Thompson series of class 12a for Monster.

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%I A058489 #27 Jun 14 2018 20:25:51
%S A058489 1,-11,-21,-55,-110,-285,-450,-1001,-1605,-2936,-4740,-8271,-12571,
%T A058489 -21075,-31755,-50104,-74600,-114816,-166570,-250601,-359499,-526106,
%U A058489 -746512,-1074840,-1501836,-2131049,-2949216,-4117846,-5647010,-7795266,-10578308,-14451212,-19455813,-26294800,-35138260
%N A058489 McKay-Thompson series of class 12a for Monster.
%C A058489 The convolution square of this sequence is A007254, except for the constant term: T12a(q)^2+22 = T6A(q^2). - _G. A. Edgar_, Apr 09 2017
%H A058489 Vaclav Kotesovec, <a href="/A058489/b058489.txt">Table of n, a(n) for n = 0..2000</a> (terms 0..1005 from G. A. Edgar)
%H A058489 D. Alexander, C. Cummins, J. McKay and C. Simons, <a href="/A007242/a007242_1.pdf">Completely Replicable Functions</a>, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy.
%H A058489 D. Ford, J. McKay and S. P. Norton, <a href="https://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).
%H A058489 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A058489 Expansion of q^(1/2) *( (eta(q)*eta(q^2)/(eta(q^3)*eta(q^6))^2 - 9*eta(q^3)*eta(q^6)/(eta(q)*eta(q^2)))^2 ) in powers of q. - _G. A. Edgar_, Apr 09 2017
%F A058489 a(n) ~ -exp(2*Pi*sqrt(n/3)) / (2*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2017
%e A058489 T12a = 1/q - 11*q - 21*q^3 - 55*q^5 - 110*q^7 - 285*q^9 - 450*q^11 - ...
%t A058489 nmax = 50; CoefficientList[Series[Product[((1-x^k) * (1-x^(2*k)) / ((1-x^(3*k)) * (1-x^(6*k))))^2, {k, 1, nmax}] - 9*x*Product[((1-x^(3*k)) * (1-x^(6*k)) / ((1-x^k) * (1-x^(2*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 08 2017 *)
%t A058489 eta[q_]:= q^(1/24)*QPochhammer[q]; b := q^(1/2)*(eta[q]*eta[q^2]/(eta[q^3]*eta[q^6]))^2; a:= CoefficientList[Series[b - 9*q/b, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 13 2018 *)
%o A058489 (PARI) q='q+O('q^30); A = (eta(q)*eta(q^2)/(eta(q^3)*eta(q^6)))^2; Vec(A - 9*q/A) \\ _G. C. Greubel_, Jun 13 2018
%Y A058489 Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K A058489 sign
%O A058489 0,2
%A A058489 _N. J. A. Sloane_, Nov 27 2000