Search: id:A007248
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%I A007248 M5084
%S A007248 1,20,62,216,641,1636,3778,8248,17277,34664,66878,125312,229252,409676,
%T A007248 716420,1230328,2079227,3460416,5677816,9198424,14729608,23328520,
%U A007248 36567242,56774712,87369461,133321908,201825396,303248408,452431503
%V A007248 1,20,-62,216,-641,1636,-3778,8248,-17277,34664,-66878,125312,-229252,
               409676,-716420,
%W A007248 1230328,-2079227,3460416,-5677816,9198424,-14729608,23328520,-36567242,
               56774712,
%X A007248 -87369461,133321908,-201825396,303248408,-452431503
%N A007248 McKay-Thompson series of class 4C for the Monster group.
%D A007248 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007248 J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. 
               Soc. 11 (1979) 308-339.
%D A007248 D. Ford, J. McKay and S. P. Norton, ``More on replicable functions,'' 
               Commun. Algebra 22, No. 13, 5175-5193 (1994).
%D A007248 J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, 
               Math. Ann., 318 (2000), 255-275.
%D A007248 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 A007248 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%F A007248 16*(theta_3/theta_2)^4 - 8 = 16/lambda(z) - 8.
%F A007248 Expansion of q*(-8 +16/lambda(z)) in powers of q^2 where nome q = exp(pi*i*z). 
               - Michael Somos Nov 14 2006
%F A007248 Expansion of q*(8 + (eta(q)/eta(q^4))^8) in powers of q^2. - Michael 
               Somos Nov 14 2006
%F A007248 Given g.f. A(x), then B(x)=A(x^2)/x satisfies 0=f(B(x), B(x^2)) where 
               f(u, v) = (v+24)^2 -(v+8)*u^2 . - Michael Somos Nov 14 2006
%e A007248 T4C = 1/q + 20*q - 62*q^3 + 216*q^5 - 641*q^7 + 1636*q^9 - 3778*q^11 
               + ...
%o A007248 (PARI) 8*x+prod(n=1,39, if(n%4,1-x^n,1),1+O(x^40))^8
%o A007248 (PARI) {a(n)=local(A); if(n<0, 0, n*=2; A=x*O(x^n); polcoeff( 8*x+(eta(x+A)/
               eta(x^4+A))^8, n))} /* Michael Somos Nov 14 2006 */
%Y A007248 A029845(2n-1) = A124972(2n-1) = a(n). - Michael Somos Nov 14 2006.
%Y A007248 Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y A007248 Sequence in context: A041784 A105092 A112144 this_sequence A117431 A159504 
               A117432
%Y A007248 Adjacent sequences: A007245 A007246 A007247 this_sequence A007249 A007250 
               A007251
%K A007248 sign,easy
%O A007248 0,2
%A A007248 N. J. A. Sloane (njas(AT)research.att.com).

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