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%I A007245 M5423
%S A007245 1,248,4124,34752,213126,1057504,4530744,17333248,60655377,197230000,
%T A007245 603096260,1749556736,4848776870,12908659008,33161242504,82505707520,
%U A007245 199429765972,469556091240,1079330385764,2426800117504,5346409013164
%N A007245 McKay-Thompson series of class 3C for Monster.
%D A007245 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007245 J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. 
               Soc. 11 (1979) 308-339.
%D A007245 N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced 
               Math., 7 (1998), 21-76, esp. p. 37.
%D A007245 D. Ford, J. McKay and S. P. Norton, ``More on replicable functions,'' 
               Commun. Algebra 22, No. 13, 5175-5193 (1994).
%D A007245 G. Hoehn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster, 
               Bonner Mathematische Schriften, Vol. 286 (1996), 1-85.
%D A007245 McKay, John; Strauss, Hubertus. The q-series of monstrous moonshine and 
               the decomposition of the head characters. Comm. Algebra 18 (1990), 
               no. 1, 253-278.
%H A007245 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%H A007245 G. Hoehn (gerald(AT)math.ksu.edu), Selbstduale Vertexoperatorsuperalgebren 
               und das Babymonster, Doctoral Dissertation, Univ. Bonn, Jul 15 1995 
               (<a href="http://www.math.ksu.edu/~gerald/papers/dr.pdf">pdf</a>, 
               <a href="http://www.math.ksu.edu/~gerald/papers/dr.ps.gz">ps</a>).
%H A007245 T. Gannon, <a href="http://arXiv.org/abs/math.QA/0402345">[math.QA/0402345] 
               Monstrous Moonshine: The first twenty-five years</a>.
%F A007245 In the notation of Gunning, Lect. on Modular Forms, pp. 53-54, expand 
               E_2(z)/Delta(z)^(1/3).
%F A007245 Given g.f. A(x), then B(x)=A(x^3)/x satisfies 0=f(B(x), B(x^2)) where 
               f(u, v)=u^3+v^3-54000+495uv-(uv)^2. - Michael Somos Apr 29 2006
%F A007245 Expansion of (phi(-q)^8 -(2phi(-q)phi(q))^4 +16phi(q)^8)/f(-q)^8 in powers 
               of q where phi(), f() are Ramanujan theta functions.
%e A007245 T3C = 1/q +248*q^2 +4124*q^5 +34752*q^8 +213126*q^11 +...
%o A007245 (PARI) a(n)=if(n<0,0,polcoeff(sum(k=1,n,240*sigma(k,3)*x^k,1+x*O(x^n))/
               eta(x+x*O(x^n))^8,n)) /* Michael Somos Apr 17 2004 */
%o A007245 (PARI) a(n)=if(n<0,0,polcoeff((x*ellj(x+x^2*O(x^n)))^(1/3),n)) /* Michael 
               Somos May 26 2004 */
%Y A007245 Sequence in context: A135046 A027654 A003916 this_sequence A030062 A033555 
               A030650
%Y A007245 Adjacent sequences: A007242 A007243 A007244 this_sequence A007246 A007247 
               A007248
%K A007245 nonn,easy,nice
%O A007245 0,2
%A A007245 N. J. A. Sloane (njas(AT)research.att.com).

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