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Search: id:A058639
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| A058639 |
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McKay-Thompson series of class 34a for the Monster group. |
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+0
2
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| 1, 1, 3, 4, 6, 7, 13, 16, 22, 29, 40, 50, 69, 83, 110, 136, 174, 214, 272, 332, 413, 502, 618, 748, 915, 1095, 1329, 1590, 1910, 2272, 2718, 3216, 3823, 4508, 5332, 6262, 7378, 8630, 10119, 11802, 13784, 16023, 18650, 21612, 25070, 28972, 33502, 38610
(list; graph; listen)
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OFFSET
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0,3
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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 (psi(q^2) * phi(q^17) - q^4 * phi(q) * psi(q^34)) / (f(-q) * f(-q^17)) in powers of q where phi(), psi(), f() are Ramanujan theta functions. - Michael Somos Dec 11 2008
Expansion of (F(q) - q^4 / F(q)) / (chi(-q) * chi(-q^17))^2 in powers of q where F(q) = G(q^17) / G(q), G(q) = chi(q) * chi(-q^2) and chi() is a Ramanujan theta function. - Michael Somos Dec 11 2008
G.f. is a period 1 Fourier series which satisfies f(-1 / (68 t)) = f(t) where q = exp(2 pi i t). - Michael Somos Dec 11 2008
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EXAMPLE
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T34a = 1/q + q + 3*q^3 + 4*q^5 + 6*q^7 + 7*q^9 + 13*q^11 + 16*q^13 + ...
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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^4 + A)^2 * eta(x^34 + A)^5 / (eta(x + A) * eta(x^2 + A) * eta(x^17 + A)^3 * eta(x^68 + A)^2) - x^4 * eta(x^2 + A)^5 * eta(x^68 + A)^2 / (eta(x + A)^3 * eta(x^4 + A)^2 * eta(x^17 + A) * eta(x^34 + A)), n))} /* Michael Somos Dec 15 2008 */
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Convolution square is A152944.
Sequence in context: A105133 A002982 A093707 this_sequence A161001 A139450 A072152
Adjacent sequences: A058636 A058637 A058638 this_sequence A058640 A058641 A058642
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KEYWORD
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nonn
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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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EXTENSIONS
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Erroneous zero at start of sequence removed by Michael Somos, Sep 30 2009
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