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A101127
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McKay-Thompson series of class 12D for the Monster group.
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0
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1, 8, 28, 64, 134, 288, 568, 1024, 1809, 3152, 5316, 8704, 13990, 22208, 34696, 53248, 80724, 121240, 180068, 264448, 384940, 556064, 796760, 1132544, 1598789, 2243056, 3127360, 4333568, 5971922, 8188096, 11170160, 15163392, 20491033
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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LINKS
| Index entries for McKay-Thompson series for Monster simple group
Eric Weisstein's World of Mathematics, Infinite Product
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FORMULA
| Expansion of q^(1/3)(eta(q^2)^2/(eta(q)eta(q^4)))^8 in powers of q.
Euler transform of period 4 sequence [8,-8,8,0,...].
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.
G.f.: (Product_{k>0} (1+x^(2k-1)))^8.
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EXAMPLE
| T12D = 1/q + 8q^2 +28q^5 +64q^8 +134q^11 +288q^14 +568q^17 +...
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PROG
| (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))
(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))
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CROSSREFS
| A007259(n)=(-1)^n*a(n).
Sequence in context: A033580 A007331 A002408 * A007259 A134747 A083013
Adjacent sequences: A101124 A101125 A101126 * A101128 A101129 A101130
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Dec 02 2004
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