|
%I #18 Jun 26 2018 09:11:31
%S 1,0,9,19,42,78,146,249,429,695,1125,1749,2713,4086,6123,8986,13122,
%T 18852,26934,38001,53328,74068,102336,140208,191153,258741,348606,
%U 466806,622383,825342,1090087,1432923,1876542,2447029,3179859,4116282,5311204,6829008
%N McKay-Thompson series of class 15C for Monster.
%H G. C. Greubel, <a href="/A058510/b058510.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 -3 + (eta(q^3)*eta(q^5)/(eta(q)*eta(q^15)))^3 in powers of q. - _G. C. Greubel_, Jun 18 2018
%F a(n) ~ exp(4*Pi*sqrt(n/15)) / (sqrt(2) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 26 2018
%e T15C = 1/q + 9*q + 19*q^2 + 42*q^3 + 78*q^4 + 146*q^5 + 249*q^6 + 429*q^7 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[-3 + (eta[q^3]*eta[q^5]/(eta[q]*eta[q^15]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 18 2018 *)
%o (PARI) q='q+O('q^50); A = -3 + (eta(q^3)*eta(q^5)/(eta(q)*eta(q^15)) )^3/q; Vec(A) \\ _G. C. Greubel_, Jun 18 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A153084 (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
|
