Search: id:A101127
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%I A101127
%S A101127 1,8,28,64,134,288,568,1024,1809,3152,5316,8704,13990,22208,34696,53248,
%T A101127 80724,121240,180068,264448,384940,556064,796760,1132544,1598789,
%U A101127 2243056,3127360,4333568,5971922,8188096,11170160,15163392,20491033
%N A101127 McKay-Thompson series of class 12D for the Monster group.
%D A101127 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. 
               Algebra 22, No. 13, 5175-5193 (1994).
%H A101127 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%H A101127 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               InfiniteProduct.html">Infinite Product</a>
%F A101127 Expansion of q^(1/3)(eta(q^2)^2/(eta(q)eta(q^4)))^8 in powers of q.
%F A101127 Euler transform of period 4 sequence [8,-8,8,0,...].
%F A101127 Given g.f. A(x), B(x)=A(x^3)/x satisfies 0=f(B(x),B(x^2)) where f(u,v)=uv(u^3+v^3) 
               -(uv)^3 +15(uv)^2 -32uv +16.
%F A101127 G.f.: (Product_{k>0} (1+x^(2k-1)))^8.
%e A101127 T12D = 1/q + 8q^2 +28q^5 +64q^8 +134q^11 +288q^14 +568q^17 +...
%o A101127 (PARI) a(n)=local(A); if(n<0,0, A=x*O(x^n); polcoeff( (eta(x^2+A)^2/eta(x+A)/
               eta(x^4+A))^8,n))
%o A101127 (PARI) a(n)=local(A); if(n<0,0, A=x*O(x^n); polcoeff( prod(k=1,(n+1)\2,
               1+x^(2*k-1),1+A)^8,n))
%Y A101127 A007259(n)=(-1)^n*a(n).
%Y A101127 Sequence in context: A033580 A007331 A002408 this_sequence A007259 A134747 
               A083013
%Y A101127 Adjacent sequences: A101124 A101125 A101126 this_sequence A101128 A101129 
               A101130
%K A101127 nonn
%O A101127 0,2
%A A101127 Michael Somos, Dec 02 2004

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