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Search: id:A062244
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| A062244 |
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McKay-Thompson series of class 36B for the Monster group. |
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5
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| 1, -1, 1, 1, -1, 0, 1, -2, 0, 2, -3, 1, 4, -4, 1, 4, -6, 1, 5, -8, 1, 8, -10, 2, 11, -14, 4, 14, -19, 4, 17, -24, 4, 23, -31, 6, 31, -40, 9, 38, -50, 10, 46, -63, 11, 60, -79, 16, 77, -98, 21, 92, -122, 24, 112, -150, 28, 140, -183, 36, 173, -224, 46, 208, -273, 54, 249, -329, 62, 304, -396, 78, 370, -478, 98
(list; graph; listen)
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OFFSET
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0,8
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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.
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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Expansion of Hauptmodul for Gamma'_0(18).
G.f.: Product_{k>0} (1+x^(6k-3))^3/(1+x^(2k-1)). - Michael Somos Mar 17 2004
Expansion of q^(1/3)eta(q)et(q^4)eta(q^6)^6/(eta(q^2)^2 eta(q^3)^3 eta(q^12)^3) in powers of q.
Given g.f. A(x), then B(x)=A(x^3)/x satisfies 0=f(B(x), B(x^2)) where f(u, v)=uv^4-u^3v^3-3u^2v^2+vu^4+4uv-2. - Michael Somos Mar 17 2004
Expansion of chi(q^3)^3 / chi(q) in powers of q where chi() is a Ramanaujan theta function.
Euler transform of period 12 sequence [ -1, 1, 2, 0, -1, -2, -1, 0, 2, 1, -1, 0, ...]. - Michael Somos Sep 17 2007
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = g(t) where q = exp(2 pi i t) and g() is g.f. for A132972.
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EXAMPLE
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T36B = 1/q - q^2 + q^5 + q^8 - q^11 + q^17 - 2*q^20 + 2*q^26 - 3*q^29 + ...
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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)^6/ eta(x^2+A)^2/ eta(x^3+A)^3/ eta(x^12+A)^3, n))} /* Michael Somos Jan 09 2005 */
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CROSSREFS
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A062242(n) = (-1)^n * a(n). A132179(n) = a(2*n). - A092848(n) = a(2*n+1). Convolution inverse of A128111.
Sequence in context: A063514 A082490 A062242 this_sequence A079957 A104513 A033769
Adjacent sequences: A062241 A062242 A062243 this_sequence A062245 A062246 A062247
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KEYWORD
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sign,easy
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AUTHOR
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njas, Jul 01 2001
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