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A058647
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McKay-Thompson series of class 36D for the Monster simple group.
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4
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1, 0, 2, 3, 4, 6, 9, 12, 16, 21, 28, 36, 47, 60, 76, 96, 120, 150, 185, 228, 280, 342, 416, 504, 608, 732, 878, 1050, 1252, 1488, 1765, 2088, 2464, 2901, 3408, 3996, 4676, 5460, 6364, 7404, 8600, 9972, 11545, 13344, 15400, 17748, 20424, 23472, 26938, 30876
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,3
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REFERENCES
| 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
| Index entries for McKay-Thompson series for Monster simple group
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FORMULA
| Expansion of q^(-1) * f(q^3) * phi(q^3) / (phi(-q^2) * psi(q^9)) in powers of q where f(), phi(), psi() are Ramanujan theta functions. - Michael Somos Feb 13 2011
Expansion of eta(q^4) * eta(q^6)^8 * eta(q^9) / (eta(q^2)^2 * eta(q^3)^3 * eta(q^12)^3 * eta(q^18)^2) in powers of q. - Michael Somos Feb 13 2011
Euler transform of period 36 sequence [ 0, 2, 3, 1, 0, -3, 0, 1, 2, 2, 0, -1, 0, 2, 3, 1, 0, -2, 0, 1, 3, 2, 0, -1, 0, 2, 2, 1, 0, -3, 0, 1, 3, 2, 0, 0, ...]. - Michael Somos Feb 13 2011
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = f(t) where q = exp(2 pi i t). - Michael Somos Feb 13 2011
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EXAMPLE
| T36D = 1/q + 2*q + 3*q^2 + 4*q^3 + 6*q^4 + 9*q^5 + 12*q^6 + 16*q^7 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^6 + A)^8 * eta(x^9 + A) / (eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 * eta(x^18 + A)^2), n))} /* Michael Somos Feb 13 2011 */
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CROSSREFS
| Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A073576 A187020 * A186115 A069907 A001935 A083365
Adjacent sequences: A058644 A058645 A058646 * A058648 A058649 A058650
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 27, 2000
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