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Search: id:A007247
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| A007247 |
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McKay-Thompson series of class 4B for Monster.
(Formerly M5305)
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+0
3
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| 1, 52, 834, 4760, 24703, 94980, 343998, 1077496, 3222915, 8844712, 23381058, 58359168, 141244796, 327974700, 742169724, 1627202744, 3490345477, 7301071680, 14987511560, 30138820888, 59623576440, 115928963656
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
McKay, John; Strauss, Hubertus. The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.
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 4q(1+k'^2)^2/(k'k^2) in powers of q^2 where k is the Jacobian elliptic modulus, k' the complementary modulus and q is the nome.
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EXAMPLE
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T4B = 1/q + 52*q + 834*q^3 + 4760*q^5 + 24703*q^7 + 94980*q^9 + ...
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, 0, A=prod(k=1, (n+1)\2, 1-x^(2*k-1), 1+x*O(x^n))^12; polcoeff(64*x/A+A, n))
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); A=(eta(x+A)/eta(x^2+A))^12; polcoeff(A+64*x/A, n))} /* Michael Somos Nov 11 2006 */
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CROSSREFS
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Sequence in context: A100413 A160344 A163691 this_sequence A083936 A160288 A133238
Adjacent sequences: A007244 A007245 A007246 this_sequence A007248 A007249 A007250
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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).
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