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Search: id:A058487
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| A058487 |
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McKay-Thompson series of class 12I for Monster. |
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+0
2
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| 1, 2, 1, 0, -2, -2, 2, 4, 3, -4, -8, -4, 5, 14, 7, -8, -20, -12, 14, 28, 17, -20, -44, -24, 28, 66, 36, -40, -90, -52, 56, 124, 71, -80, -176, -96, 109, 244, 133, -144, -326, -182, 198, 432, 240, -268, -580, -316, 349, 772, 420, -456, -1004, -552, 600, 1300, 713, -780, -1692, -916, 1001, 2186, 1182
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Euler transform of period 6 sequence [2,-2,0,-2,2,0,...]. - Michael Somos Mar 18 2004
G.f. A(x) satisfies 0=f(A(x^2)/x,A(x^4)/x^2) where f(u,v)=u^2+3v-u^2v+v^2. - Michael Somos Mar 18 2004
Expansion of q(eta(q^4)^4*eta(q^6)^2/(eta(q^2)^2*eta(q^12)^4)) in powers of q^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.
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FORMULA
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G.f.: ( Product_{k>0} (1-x^(6k-2))(1-x^(6k-4))/((1-x^(6k-1))(1-x^(6k-5))) )^2.
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EXAMPLE
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eta(4z)^4*eta(6z)^2/(eta(2z)^2*eta(12z)^4) = 1/q + 2*q^1 + 1*q^3 - 2*q^7 - 2*q^9 + 2*q^11 + 4*q^13 + 3*q^15 + ...
T12I = 1/q + 2*q + 1*q^3 - 2*q^7 - 2*q^9 + 2*q^11 + 4*q^13 + 3*q^15 + ...
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PROGRAM
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(PARI) a(n)=local(A, m); if(n<-1, 0, n++; A=1+O(x); m=1; while(m<=n, m*=2; A=subst(A, x, x^2); A=sqrt(A*(A+3*x)/(A-x))); polcoeff(A, n))
(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff((eta(x^2+A)^2*eta(x^3+A)/eta(x+A)/eta(x^6+A)^2)^2, n))
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
A062243(n)=(-1)^n*a(n).
Sequence in context: A029343 A137992 A047654 this_sequence A062243 A128095 A097854
Adjacent sequences: A058484 A058485 A058486 this_sequence A058488 A058489 A058490
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KEYWORD
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sign
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AUTHOR
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njas, Nov 27 2000
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