Search: id:A058688
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%I A058688
%S A058688 1,0,0,1,1,1,1,1,2,2,2,2,3,3,3,4,5,5,5,6,7,8,8,10,12,12,13,15,17,18,19,
%T A058688 22,25,27,28,32,36,38,41,46,51,54,58,64,71,76,81,89,99,105,112,123,134,
%U A058688 143,153,167,182,194,207,225,244,260,277,301,325,346,369,398,429,458
%V A058688 1,0,0,-1,1,-1,1,-1,2,-2,2,-2,3,-3,3,-4,5,-5,5,-6,7,-8,8,-10,12,-12,13,
               -15,17,-18,19,
%W A058688 -22,25,-27,28,-32,36,-38,41,-46,51,-54,58,-64,71,-76,81,-89,99,-105,112,
               -123,134,-143,
%X A058688 153,-167,182,-194,207,-225,244,-260,277,-301,325,-346,369,-398,429,-458
%N A058688 McKay-Thompson series of class 46A for the Monster group.
%C A058688 Also McKay-Thompson series of class 46B for the Monster group.
%D A058688 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. 
               Algebra 22, No. 13, 5175-5193 (1994).
%H A058688 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%F A058688 Expansion of 1+(1/q)chi(-q)chi(-q^23) in powers of q where chi() is a 
               Ramanujan theta function. - Michael Somos Jun 07 2006
%F A058688 G.f.: 1 + (1/x)*Product_{k>0} 1/((1+x^k)(1+x^(23k))).
%F A058688 G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= v^2 -v +2 -2*u +u^2 
               -v*u^2 . - Michael Somos Feb 14 2007
%e A058688 T46A = 1/q -q^2 +q^3 -q^4 +q^5 -q^6 +2*q^7 -2*q^8 +2*q^9 +...
%o A058688 (PARI) {a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff( x+ eta(x+A)*eta(x^23+A)/ 
               eta(x^2+A)/eta(x^46+A), n))} /* Michael Somos Feb 14 2007 */
%Y A058688 Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y A058688 Sequence in context: A000700 A081362 A112216 this_sequence A132322 A018118 
               A029084
%Y A058688 Adjacent sequences: A058685 A058686 A058687 this_sequence A058689 A058690 
               A058691
%K A058688 sign
%O A058688 -1,9
%A A058688 N. J. A. Sloane (njas(AT)research.att.com), Nov 27, 2000

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