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Search: id:A062243
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| A062243 |
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McKay-Thompson series of class 24c for the Monster group. |
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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 12 sequence [ -2,0,0,-2,-2,0,-2,-2,0,0,-2,0,...]. - Michael Somos May 14 2004
Expansion of Hauptmodul for Gamma'_0(12).
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REFERENCES
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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^(4k))(1-x^(2k-1))/(1-x^(3k)) )^2.
Given G.f. A(x), then B(x)=A(x^2)^2/(3x^2) satisfies 0=f(B(x), B(x^2)) where f(u, v)= (u+v)^2(u^2+v^2-uv) +3(u^3+v^3)(1+uv) -9uv(1+(uv)^2) -90(uv)^2 -27uv(u+v)(1+uv). - Michael Somos May 14 2004
Expansion of q^(1/2)(eta(q)eta(q^4)eta(q^6)/(eta(q^2)eta(q^3)eta(q^12)))^2 in powers of q.
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EXAMPLE
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T24c = 1/q -2*q +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); if(n<0, 0, A=x*O(x^n); polcoeff((eta(x+A)*eta(x^4+A)*eta(x^6+A)/eta(x^2+A)/eta(x^3+A)/eta(x^12+A))^2, n))
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CROSSREFS
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A058487(n)=(-1)^n*a(n).
Adjacent sequences: A062240 A062241 A062242 this_sequence A062244 A062245 A062246
Sequence in context: A137992 A047654 A058487 this_sequence A128095 A097854 A019591
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KEYWORD
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sign
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AUTHOR
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njas, Jul 01 2001
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