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Search: id:A112199
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| A112199 |
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McKay-Thompson series of class 57A for the Monster group. |
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+0
2
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| 1, 1, 1, 1, 3, 2, 4, 4, 5, 6, 8, 9, 12, 13, 16, 18, 23, 25, 31, 36, 43, 48, 57, 64, 76, 86, 99, 112, 131, 146, 169, 190, 217, 243, 278, 310, 353, 394, 446, 498, 562, 624, 704, 781, 877, 972, 1088, 1204, 1345, 1488, 1656, 1829, 2033, 2240, 2486, 2738, 3030, 3334
(list; graph; listen)
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OFFSET
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0,5
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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).
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.5).
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339. See page 336.
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FORMULA
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G.f.: G(x) * G(x^19) + x^4 * H(x) * H(x^19) where G() is g.f. of A003114 and H() is g.f. of A003106.
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EXAMPLE
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T57A = 1/q +q^2 +q^5 +q^8 +3*q^11 +2*q^14 +4*q^17 +4*q^20 +...
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PROGRAM
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(PARI) {a(n) = local(A, A1, A2); if( n<0, 0, n = 2*n ; A = x^3 * O(x^n) ; A1 = ( eta(x + A) * eta(x^19 + A) / eta(x^2 + A) / eta(x^38 + A) )^2; A2 = -subst(A1, x, -x); polcoeff( x^4 / A1 / A2 - (A1 + A2) / 4 / x, n))} /* Michael Somos Jan 07 2008 */
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CROSSREFS
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Cf. A136569.
Sequence in context: A061901 A078822 A069745 this_sequence A059851 A047993 A033177
Adjacent sequences: A112196 A112197 A112198 this_sequence A112200 A112201 A112202
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 28 2005
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