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Search: id:A058688
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| A058688 |
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McKay-Thompson series of class 46A for the Monster group. |
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+0
2
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| 1, 0, 0, -1, 1, -1, 1, -1, 2, -2, 2, -2, 3, -3, 3, -4, 5, -5, 5, -6, 7, -8, 8, -10, 12, -12, 13, -15, 17, -18, 19, -22, 25, -27, 28, -32, 36, -38, 41, -46, 51, -54, 58, -64, 71, -76, 81, -89, 99, -105, 112, -123, 134, -143, 153, -167, 182, -194, 207, -225, 244, -260, 277, -301, 325, -346, 369, -398, 429, -458
(list; graph; listen)
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OFFSET
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-1,9
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COMMENT
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Also McKay-Thompson series of class 46B for the Monster group.
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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).
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FORMULA
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Expansion of 1+(1/q)chi(-q)chi(-q^23) in powers of q where chi() is a Ramanujan theta function. - Michael Somos Jun 07 2006
G.f.: 1 + (1/x)*Product_{k>0} 1/((1+x^k)(1+x^(23k))).
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= v^2 -v +2 -2*u +u^2 -v*u^2 . - Michael Somos Feb 14 2007
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EXAMPLE
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T46A = 1/q -q^2 +q^3 -q^4 +q^5 -q^6 +2*q^7 -2*q^8 +2*q^9 +...
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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( x+ eta(x+A)*eta(x^23+A)/ eta(x^2+A)/eta(x^46+A), n))} /* Michael Somos Feb 14 2007 */
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A000700 A081362 A112216 this_sequence A132322 A018118 A029084
Adjacent sequences: A058685 A058686 A058687 this_sequence A058689 A058690 A058691
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KEYWORD
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sign
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AUTHOR
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njas, Nov 27, 2000
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