%I A058578
%S A058578 1,2,5,8,14,22,34,52,75,108,152,212,293,398,539,720,956,1260,1646,2140,
%T A058578 2761,3548,4532,5760,7292,9186,11532,14416,17958,22292,27576,34012,
%U A058578 41815,51264,62672,76416,92941,112756,136481,164816,198602,238810
%N A058578 McKay-Thompson series of class 24H for Monster.
%D A058578 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. 
               Algebra 22, No. 13, 5175-5193 (1994).
%H A058578 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%F A058578 Given g.f. A(x), then B(x)=A(x^2)^2/x^2 satisfies 0=f(B(x), B(x^2)) where 
               f(u, v)= -uv(1+u^2v^2) +7uv(u+v)(1+uv) +9uv(u^2+v^2). - Michael Somos 
               May 16 2004
%F A058578 Expansion of q^(1/2)(eta(q^3)eta(q^4)/(eta(q)eta(q^12)))^2 in powers 
               of q. - Michael Somos May 16 2004
%F A058578 Euler transform of period 12 sequence [2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 
               2, 0, ...]. - Michael Somos May 16 2004
%e A058578 T24H = 1/q + 2*q + 5*q^3 + 8*q^5 + 14*q^7 + 22*q^9 + 34*q^11 + 52*q^13 
               + ...
%o A058578 (PARI) a(n)=local(A); if(n<0,0,A=x*O(x^n); polcoeff((eta(x^3+A)*eta(x^4+A)/
               eta(x+A)/eta(x^12+A))^2,n)) /* Michael Somos May 16 2004 */
%Y A058578 Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y A058578 Sequence in context: A165189 A011842 A000094 this_sequence A023674 A139218 
               A017988
%Y A058578 Adjacent sequences: A058575 A058576 A058577 this_sequence A058579 A058580 
               A058581
%K A058578 nonn
%O A058578 0,2
%A A058578 N. J. A. Sloane (njas(AT)research.att.com), Nov 27, 2000