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Search: id:A058548
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| A058548 |
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McKay-Thompson series of class 18j for Monster. |
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+0
1
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| 1, 0, 1, -2, 0, 2, 1, 0, 3, 2, 0, 2, -4, 0, 1, 0, 0, 2, 7, 0, 4, -10, 0, 8, 3, 0, 8, 10, 0, 8, -15, 0, 7, 2, 0, 10, 22, 0, 17, -32, 0, 22, 10, 0, 26, 32, 0, 24, -48, 0, 25, 8, 0, 30, 62, 0, 43, -88, 0, 58, 22, 0, 65, 88, 0, 66, -127, 0, 66, 22, 0, 80, 152, 0, 107, -214, 0, 136, 52, 0
(list; graph; listen)
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OFFSET
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-1,4
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COMMENT
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G.f. A(x) satisfies 0=f(A(x),A(x^2))=f(A(x),A(-x)) where f(u,v)= 32+4(u+v)-2(u^2+v^2)+2(u^3+v^3)-3uv(u+v)+(u^4+v^4)+uv(u^2+v^2)-(uv)^2(u+v). - Michael Somos Apr 20 2004
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REFERENCES
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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
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Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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a(3n)=0.
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EXAMPLE
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T18j = 1/q + q - 2*q^2 + 2*q^4 + q^5 + 3*q^7 + 2*q^8 + 2*q^10 - 4*q^11 + ...
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, n==-1, A=x^2*O(x^n); A=((eta(x^3+A)*eta(x^18+A)^2*eta(x^27+A))/(eta(x^6+A)*eta(x^9+A)^2*eta(x^54+A)))\ ^2/x; polcoeff(A+1/A, n)) /* Michael Somos Apr 20 2004 */
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A036849 A097364 A074905 this_sequence A157030 A080844 A076626
Adjacent sequences: A058545 A058546 A058547 this_sequence A058549 A058550 A058551
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 27, 2000
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