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Search: id:A136560
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| A136560 |
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McKay-Thompson series of class 49a for the Monster group with a(0) = 3. |
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+0
1
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| 1, 3, 2, 1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 19, 25, 28, 35, 41, 50, 58, 71, 81, 98, 113, 134, 154, 183, 208, 244, 280, 326, 371, 431, 489, 565, 641, 735, 832, 953, 1075, 1225, 1382, 1569, 1764, 1999, 2243, 2533, 2839, 3195, 3575, 4018, 4484, 5026, 5604, 6267, 6975
(list; graph; listen)
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OFFSET
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-1,2
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COMMENT
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Denoted 49Z in Conway+Norton with a slight typo in the formula on page 337.
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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.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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FORMULA
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Expansion of ( eta(q^4)^4 + 7 * eta(q)^2 * eta(q^49)^2 ) / ( eta(q) * eta(q^49) * ( eta(q)^2 + 7 * eta(q) * eta(q^49) + 7 * eta(q^49)^2 ) ) in powers of q.
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EXAMPLE
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1/q + 3 + 2*q + q^2 + 2*q^3 + 3*q^4 + 4*q^5 + 5*q^6 + 7*q^7 + 8*q^8 + ...
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PROGRAM
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(PARI) {a(n) = local(A, A1, A2, A3); if( n<-1, 0, n++; A = x * O(x^n); A1 = eta(x + A); A2 = eta(x^7 + A); A3 = eta(x^49 + A); polcoeff( (A2^4 + 7 * x^3 * A1^2 * A3^2) / (A1 * A3) / (A1^2 + 7 * x^2 * A1*A3 + 7 * x^4 * A3^2 ), n))}
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CROSSREFS
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Cf. A058700(n) = a(n) unless n=0.
Adjacent sequences: A136557 A136558 A136559 this_sequence A136561 A136562 A136563
Sequence in context: A036583 A047878 A120441 this_sequence A105847 A048984 A136531
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jan 05 2008
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