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Search: id:A082304
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| A082304 |
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McKay-Thompson series of class 16d for the Monster group. |
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+0
2
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| 1, -2, -1, 2, 3, -2, -4, 4, 5, -8, -8, 10, 11, -12, -15, 18, 22, -26, -29, 34, 38, -42, -51, 56, 66, -78, -85, 98, 109, -120, -139, 156, 176, -202, -222, 250, 279, -306, -346, 384, 429, -482, -530, 590, 650, -714, -797, 876, 972, -1080, -1180, 1304, 1431, -1562, -1728, 1892, 2078, -2290, -2496
(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).
J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275. see page 273.
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FORMULA
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G.f.: ( Product_{n>0} (1-x^n)/(1-x^(4n)) )^2.
Given g.f. A(x), then B(x)=A(x^4)/x satisfies 0=f(B(x), B(x^2)) where f(u, v)=-v^2 +16uv +16u^2 +256u +u^2v. - Michael Somos May 14 2004
Expansion of q^(1/4)*(eta(q)/ eta(q^4))^2 in powers of q.
Expansion of phi(-q)/ psi(q^2) in powers of q where phi(), psi() are Ramanujan theta functions.
Euler transform of period 4 sequence [ -2, -2, -2, 0, ...].
Given g.f. A(x), then B(x)=A(x^4)/x satisfies 0=f(B(x), B(x^3)) where f(u, v)= (u^2+v^2)^2 -u*v* (4+u*v)^2. - Michael Somos Aug 13 2007
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EXAMPLE
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T16d = 1/q - 2*q^3 - q^7 + 2*q^11 + 3*q^15 - 2*q^19 - 4*q^23 +...
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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+A)/ eta(x^4+A))^2, n))}
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CROSSREFS
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A029839(n)= (-1)^n* a(n).
Adjacent sequences: A082301 A082302 A082303 this_sequence A082305 A082306 A082307
Sequence in context: A096920 A087154 A029839 this_sequence A035368 A107853 A054758
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 08 2003
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