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Search: id:A058578
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| A058578 |
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McKay-Thompson series of class 24H for Monster. |
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+0
1
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| 1, 2, 5, 8, 14, 22, 34, 52, 75, 108, 152, 212, 293, 398, 539, 720, 956, 1260, 1646, 2140, 2761, 3548, 4532, 5760, 7292, 9186, 11532, 14416, 17958, 22292, 27576, 34012, 41815, 51264, 62672, 76416, 92941, 112756, 136481, 164816, 198602, 238810
(list; graph; listen)
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OFFSET
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0,2
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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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Given g.f. A(x), then B(x)=A(x^2)^2/x^2 satisfies 0=f(B(x), B(x^2)) where f(u, v)= -uv(1+u^2v^2) +7uv(u+v)(1+uv) +9uv(u^2+v^2). - Michael Somos May 16 2004
Expansion of q^(1/2)(eta(q^3)eta(q^4)/(eta(q)eta(q^12)))^2 in powers of q. - Michael Somos May 16 2004
Euler transform of period 12 sequence [2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, ...]. - Michael Somos May 16 2004
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EXAMPLE
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T24H = 1/q + 2*q + 5*q^3 + 8*q^5 + 14*q^7 + 22*q^9 + 34*q^11 + 52*q^13 + ...
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff((eta(x^3+A)*eta(x^4+A)/eta(x+A)/eta(x^12+A))^2, n)) /* Michael Somos May 16 2004 */
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A165189 A011842 A000094 this_sequence A023674 A139218 A017988
Adjacent sequences: A058575 A058576 A058577 this_sequence A058579 A058580 A058581
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KEYWORD
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nonn
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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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