|
%I M5302 #28 May 11 2018 01:50:54
%S 1,0,51,204,681,1956,5135,12360,28119,60572,125682,251040,487426,
%T 920568,1699611,3070508,5445510,9490116,16283793,27537708,45959775,
%U 75760640,123471327,199081632,317814988
%N McKay-Thompson series of class 7A for Monster.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A007264/b007264.txt">Table of n, a(n) for n = -1..10000</a>
%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%H N. D. Elkies, <a href="http://www.math.harvard.edu/~elkies/modular.pdf">Elliptic and modular curves over finite fields and related computational issues</a>, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 39.
%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 J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of (h+7)^2/h, where h = (eta(q)/eta(q^7))^4.
%F a(n) ~ exp(4*Pi*sqrt(n/7)) / (sqrt(2) * 7^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Dec 04 2015
%e T7A = 1/q + 51*q + 204*q^2 + 681*q^3 + 1956*q^4 + 5135*q^5 + 12360*q^6 + ...
%t QP = QPochhammer; h = q*(QP[q^7]/QP[q])^4; s = 1 - 10*q + q*((1+7*h)^2/h - 1/q) + O[q]^30; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 15 2015 *)
%o (PARI) q='q+O('q^50); F =(eta(q)/eta(q^7))^4/q; Vec(F*(1 + 7/F)^2 - 10) \\ _G. C. Greubel_, May 10 2018
%Y Essentially same as A045489 and A030183.
%K nonn
%O -1,3
%A _N. J. A. Sloane_
|
