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Search: id:A112146
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| A112146 |
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McKay-Thompson series of class 9b for the Monster group. |
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+0
4
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| 1, 0, 9, -4, 0, 36, 2, 0, 126, 12, 0, 324, -21, 0, 801, 4, 0, 1764, 36, 0, 3744, -68, 0, 7452, 21, 0, 14400, 112, 0, 26748, -184, 0, 48510, 44, 0, 85536, 275, 0, 147924, -456, 0, 250452, 112, 0, 417276, 644, 0, 683640, -1019, 0, 1104948, 240, 0, 1761552, 1370, 0
(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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LINKS
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Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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Expansion of q^(1/3)* 3*( b(q)/ c(q)+ c(q)/ b(q)) in powers of q where b(), c() are cubic AGM analog functions. - Michael Somos Mar 24 2007
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (u+v)^3 -(u^2 +3*u -18)* (v^2+ 3*v -18) .
G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= +u^2 +w^2 +u*w +18*(u+w) -(w+u)*v^2 -9*v +54 .
Expansion of ( (eta(q^3) / eta(q^9))^4 + 9 * (eta(q^9) / eta(q^3))^4) in powers of q.
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EXAMPLE
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T9b = 1/q +9*q -4*q^2 +36*q^4 +2*q^5 +126*q^7 +12*q^8 +...
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PROGRAM
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(PARI) {a(n)= local(A); if(n<-1, 0, n++; A= x*O(x^n); A= (eta(x^3+A)/ eta(x^9+A))^4; polcoeff( A +9*x^2/A, n))} /* Michael Somos Mar 24 2007 */
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
A058095(n)= a(3n-1). 9*A128758(n)= a(3n+1).
Sequence in context: A119516 A116393 A021918 this_sequence A056897 A010158 A098454
Adjacent sequences: A112143 A112144 A112145 this_sequence A112147 A112148 A112149
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 28 2005, Aug 09 2008
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