Search: id:A007259
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%I A007259 M4504
%S A007259 1,8,28,64,134,288,568,1024,1809,3152,5316,8704,13990,22208,34696,53248,
               80724,
%T A007259 121240,180068,264448,384940,556064,796760,1132544,1598789,2243056,3127360,
%U A007259 4333568,5971922,8188096,11170160,15163392,20491033,27572936
%V A007259 1,-8,28,-64,134,-288,568,-1024,1809,-3152,5316,-8704,13990,-22208,34696,
               -53248,80724,
%W A007259 -121240,180068,-264448,384940,-556064,796760,-1132544,1598789,-2243056,
               3127360,
%X A007259 -4333568,5971922,-8188096,11170160,-15163392,20491033,-27572936
%N A007259 Expansion of Product (1+q^m)^(-8); m=1..inf.
%C A007259 McKay-Thompson series of class 6F for the Monster group.
%D A007259 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007259 T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 
               2nd. ed. 1949, p. 118, Problem 24.
%D A007259 J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. 
               Soc. 11 (1979) 308-339.
%D A007259 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. 
               Algebra 22, No. 13, 5175-5193 (1994).
%D A007259 J. McKay and H. Strauss, The q-series of monstrous moonshine and the 
               decomposition of the head characters. Comm. Algebra 18 (1990), no. 
               1, 253-278.
%H A007259 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%F A007259 Expansion of chi(-q)^8 in powers of q where chi() is a Ramanujan theta 
               function. - Michael Somos Aug 18 2007
%F A007259 Expansion of q^(-1/3) * (eta(q) / eta(q^2))^8 in powers of q. - Michael 
               Somos Aug 18 2007
%F A007259 Euler transform of period 2 sequence [ -8, 0, ...]. - Michael Somos Aug 
               18 2007
%F A007259 Given g.f. A(x), then B(x) = A(x^3)/x satisfies 0 = f(B(x), B(x^2)) where 
               f(u, v) = v^2 - u^2 * v - 16 * u. - Michael Somos Aug 18 2007
%F A007259 G.f. is a Fourier series which satisfies f(-1/(2 t)) = 16/ f(t) where 
               q = exp(2 pi i t). - Michael Somos Aug 18 2007
%e A007259 T6F = 1/q - 8q^2 + 28q^5 - 64q^8 + 134q^11 - 288q^14 + 568q^17 + ...
%o A007259 (PARI) {a(n)=local(A); if(n<0,0, A=x*O(x^n); polcoeff( (eta(x+A)/eta(x^2+A))^8, 
               n))}
%Y A007259 Sequence in context: A007331 A002408 A101127 this_sequence A134747 A083013 
               A028553
%Y A007259 Adjacent sequences: A007256 A007257 A007258 this_sequence A007260 A007261 
               A007262
%K A007259 sign,easy,nice
%O A007259 0,2
%A A007259 N. J. A. Sloane (njas(AT)research.att.com).

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