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 A007252 McKay-Thompson series of class 5B for Monster. (Formerly M4599) 2

%I M4599

%S 1,0,9,10,-30,6,-25,96,60,-250,45,-150,544,360,-1230,184,-675,2310,

%T 1410,-4830,750,-2450,8196,4920,-16180,2376,-7875,25644,15000,-48720,

%U 7126,-22800,73221,42310,-134760,19284,-61400,194334,110610,-349000,49563,-155250,486370

%N McKay-Thompson series of class 5B for Monster.

%C G.f. A(x) satisfies 0=f(A(x)-6,A(x^2)-6) where f(u,v)=u^3+v^3-125uv-12uv(u+v)-(uv)^2. - Michael Somos Apr 30 2004

%C Expansion of 6+(eta(q)/eta(q^5))^6 in powers of q. - Michael Somos Apr 30 2004

%D J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%D D. Ford, J. McKay and S. P. Norton, ``More on replicable functions,'' Commun. Algebra 22, No. 13, 5175-5193 (1994).

%D 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.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%e T5B = 1/q + 9*q + 10*q^2 - 30*q^3 + 6*q^4 - 25*q^5 + 96*q^6 + 60*q^7 - ...

%o (PARI) a(n)=local(A); if(n<-1,0,n++; A=x*O(x^n); polcoeff(6*x+(eta(x+A)/eta(x^5+A))^6,n)) /* Michael Somos Apr 30 2004 */

%o (PARI) a(n)=local(A,k); if(n<-1,0, k=(sqrtint(40*n+48)+7)\10; A=x*(sum(i=-k,k,(-1)^i*x^((5*i^2+3*i)/2),x^2*O(x^n))/sum(i=-k,k,(-1)^i*x^((5*i^2+i)/2),x^2*O(x^n)))^5; polcoeff(1/A-A-5,n)) /* Michael Somos Apr 30 2004 */

%Y Cf. A045483 (same except for initial terms).

%K sign

%O -1,3

%A _N. J. A. Sloane_.

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