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Search: id:A058095
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| A058095 |
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McKay-Thompson series of class 9c for the Monster group. |
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+0
2
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| 1, -4, 2, 12, -21, 4, 36, -68, 21, 112, -184, 44, 275, -456, 112, 644, -1019, 240, 1370, -2156, 514, 2828, -4340, 992, 5498, -8392, 1930, 10428, -15675, 3528, 19060, -28472, 6399, 34072, -50382, 11184, 59333, -87260, 19312, 101496, -148148, 32480, 170130, -247156
(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).
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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) in powers of q where b(), c() are cubic AGM analog functions.
Expansion of q^(1/3)* (eta(q)/ eta(q^3))^4 in powers of q. - Michael Somos Mar 24 2007
Given g.f. A(x), then B(x)= 1/x* A(x^3) satisfies 0= f(B(x), B(x^2)) where f(u, v)= (u+v)^3 -u*v* (u+3)* (v+3) .
Given g.f. A(x), then B(x)= 1/x* A(x^3) satisfies 0= f(B(x), B(x^2), B(x^4)) where f(u, v, w)= u^2*v^2 +v^2*w^2 -v*u^2*w^2 +u*w*v^2 -9*u*w* (u+w) .
G.f.: (Product_{k>0} (1 +x^k +x^(2k)) )^-4 .
Euler transform of period 3 sequence [ -4, -4, 0, ...]. - Michael Somos Mar 24 2007
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EXAMPLE
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T9c = 1/q - 4*q^2 + 2*q^5 + 12*q^8 - 21*q^11 + 4*q^14 + 36*q^17 - 68*q^20 + ...
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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^3+A))^4, n))} /* Michael Somos Mar 24 2007 */
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
A112146(3n-1)= a(n). Convolution inverse of A128758.
Sequence in context: A019239 A143944 A154345 this_sequence A105196 A167557 A069836
Adjacent sequences: A058092 A058093 A058094 this_sequence A058096 A058097 A058098
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 27 2000
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