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Search: id:A022597
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| A022597 |
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Expansion of Product (1+q^m)^(-2); m=1..inf. |
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+0
3
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| 1, -2, 1, -2, 4, -4, 5, -6, 9, -12, 13, -16, 21, -26, 29, -36, 46, -54, 62, -74, 90, -106, 122, -142, 171, -200, 227, -264, 311, -358, 408, -470, 545, -626, 709, -810, 933, -1062, 1198, -1362, 1555, -1760, 1980, -2238, 2536, -2858, 3205, -3602, 4063, -4560, 5092, -5704, 6400, -7150, 7966
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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McKay-Thompson series of class 24J for the Monster group.
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REFERENCES
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T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 116, q_2^2.
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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T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for McKay-Thompson series for Monster simple group
D. Foata and G.-N. Han, Jacobi and Watson Identities Combinatorially Revisited
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FORMULA
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Expansion of q^(1/12)(eta(q)/eta(q^2))^2 in powers of q.
Euler transform of period 2 sequence [ -2, 0, ...]. - Michael Somos Sep 10 2005
Expansion of chi(-q)^2 in powers of q where chi() is a Ramanujan theta function.
G.f. is a period 1 Fourier series which satisfies f(-1/(288 t)) = 2 / f(t) where q = exp(2 pi i t).
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EXAMPLE
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T24J = 1/q - 2*q^11 + q^23 - 2*q^35 + 4*q^47 - 4*q^59 + 5*q^71 - 6*q^83 + ...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x+A)/eta(x^2+A))^2, n))} /* Michael Somos Sep 10 2005 */
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CROSSREFS
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a(n)=(-1)^n*A073252(n).
Convolution square of A081362. Convolution inverse of A022567.
Sequence in context: A108802 A023673 A132965 this_sequence A073252 A134005 A132320
Adjacent sequences: A022594 A022595 A022596 this_sequence A022598 A022599 A022600
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KEYWORD
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sign,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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