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Search: id:A058486
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| A058486 |
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McKay-Thompson series of class 12H for Monster. |
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+0
1
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| 1, 0, 14, 36, 85, 180, 360, 684, 1246, 2196, 3754, 6264, 10226, 16380, 25804, 40032, 61275, 92628, 138452, 204804, 300040, 435672, 627356, 896400, 1271525, 1791324, 2507426, 3488472, 4825531, 6638688, 9085888, 12373992, 16772908, 22633812
(list; graph; listen)
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OFFSET
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-1,3
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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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FORMULA
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Given g.f. A(x), then B(x)=A(x)+4 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 (eta(q^3)eta(q^4)/(eta(q)eta(q^12)))^4-4 in powers of q. - Michael Somos May 16 2004
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EXAMPLE
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T12H = 1/q + 14*q + 36*q^2 + 85*q^3 + 180*q^4 + 360*q^5 + 684*q^6 + ...
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PROGRAM
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(PARI) a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff((eta(x^3+A)*eta(x^4+A)/eta(x+A)/eta(x^12+A))^4-4*x, n)) /* Michael Somos May 16 2004 */
(PARI) a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff(eta(x^2+A)^6*eta(x^6+A)^6/eta(x+A)^5/eta(x^3+A)/eta(x^4+A)/eta(x^12+A)^5-5*x, 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: A104317 A115664 A024814 this_sequence A113627 A121319 A034181
Adjacent sequences: A058483 A058484 A058485 this_sequence A058487 A058488 A058489
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KEYWORD
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nonn
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AUTHOR
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njas, Nov 27 2000
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