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Search: id:A138688
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| A138688 |
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McKay-Thompson series of class 24I for the Monster group with a(0) = 2. |
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1
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| 1, 2, 4, 6, 11, 18, 28, 42, 62, 90, 128, 180, 250, 342, 464, 624, 831, 1098, 1440, 1878, 2432, 3132, 4012, 5112, 6485, 8190, 10300, 12900, 16097, 20016, 24804, 30636, 37724, 46314, 56700, 69228, 84302, 102402, 124088, 150024, 180973, 217836
(list; graph; listen)
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OFFSET
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-1,2
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REFERENCES
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J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339. See page 335.
K. Bringmann and H. Swisher, On a conjecture of Koike on identities between Thompson series and Roger-Ramanujan functions, Proc. Amer. Math. Soc. 135 (2007), 2317-2326. See page 2325 (A.7)
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FORMULA
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Expansion of psi(q^4) * phi(-q^3) / (phi(-q) * psi(q^12)) in powers of q where phi(), psi() are Ramanujan theta functions.
Expansion of eta(q^2) * eta(q^3)^2 * eta(q^8)^2 * eta(q^12) / (eta(q)^2 * eta(q^4) * eta(q^6) * eta(q^24)^2) in powers of q.
Euler transform of period 24 sequence [ 2, 1, 0, 2, 2, 0, 2, 0, 0, 1, 2, 0, 2, 1, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0, ...].
G.f.: (G(x) * G(x^24) + x^5 * H(x) * H(x^24))^2 * (G(x^4) * G(x^6) + x^2 * H(x^4) * H(x^6)) where G() is g.f. of A003114 and H() is g.f. of A003106.
G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
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1/q + 2 + 4*q + 6*q^2 + 11*q^3 + 18*q^4 + 28*q^5 + 42*q^6 + 62*q^7 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^8 + A)^2 * eta(x^12 + A) / (eta(x + A)^2 * eta(x^4 + A) * eta(x^6 + A) * eta(x^24 + A)^2), n))}
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CROSSREFS
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A058579(n) = a(n) unless n=0.
Sequence in context: A034297 A026636 A026658 this_sequence A131298 A007053 A005684
Adjacent sequences: A138685 A138686 A138687 this_sequence A138689 A138690 A138691
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 26 2008
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