|
%I
%S 1,0,9,-4,0,36,2,0,126,12,0,324,-21,0,801,4,0,1764,36,0,3744,-68,0,
%T 7452,21,0,14400,112,0,26748,-184,0,48510,44,0,85536,275,0,147924,
%U -456,0,250452,112,0,417276,644,0,683640,-1019,0,1104948,240,0,1761552,1370,0
%N McKay-Thompson series of class 9b for the Monster group.
%D D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of q^(1/3)* 3*( b(q)/ c(q)+ c(q)/ b(q)) in powers of q where b(), c() are cubic AGM analog functions. - Michael Somos Mar 24 2007
%F G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (u+v)^3 -(u^2 +3*u -18)* (v^2+ 3*v -18) .
%F G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= +u^2 +w^2 +u*w +18*(u+w) -(w+u)*v^2 -9*v +54 .
%F Expansion of ( (eta(q^3) / eta(q^9))^4 + 9 * (eta(q^9) / eta(q^3))^4) in powers of q.
%e T9b = 1/q +9*q -4*q^2 +36*q^4 +2*q^5 +126*q^7 +12*q^8 +...
%o (PARI) {a(n)= local(A); if(n<-1, 0, n++; A= x*O(x^n); A= (eta(x^3+A)/ eta(x^9+A))^4; polcoeff( A +9*x^2/A, n))} /* Michael Somos Mar 24 2007 */
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y A058095(n)= a(3n-1). 9*A128758(n)= a(3n+1).
%K sign
%O -1,3
%A Michael Somos, Aug 28 2005, Aug 09 2008
|
