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Search: id:A007267
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| A007267 |
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Expansion of 16(1+k^2)^4/(kk'^2)^2 in powers of q where k is the Jacobian elliptic modulus, k' the complementary modulus and q is the nome.
(Formerly M5369)
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+0
199
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| 1, 104, 4372, 96256, 1240002, 10698752, 74428120, 431529984, 2206741887, 10117578752, 42616961892, 166564106240, 611800208702, 2125795885056, 7040425608760, 22327393665024, 68134255043715, 200740384538624
(list; graph; listen)
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OFFSET
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-1,2
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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. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 195.
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).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.
R. Fricke, Die elliptischen Funktionen und ihre Anwendungen, Teubner, 1922, Vol. 2, see p. 517.
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LINKS
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T. D. Noe, Table of n, a(n) for n=-1..1000
Index entries for McKay-Thompson series for Monster simple group
R. Fricke, Die elliptischen Funktionen und ihre Anwendungen, Vol. 2.
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FORMULA
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Expansion of 16(1+k'^2)^4/(k'k^2)^2 in powers of q^2. - Michael Somos Nov 11 2006
McKay-Thompson series of class 2A for Monster except for a(0).
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PROGRAM
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(PARI) a(n)=local(A); if(n<-1, 0, A=prod(k=1, n\2+1, 1-x^(2*k-1), 1+x^2*O(x^n))^12; polcoeff((64*x/A+A)^2, n+1))
(PARI) {a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); A=(eta(x+A)/eta(x^2+A))^12; polcoeff((A+64*x/A)^2, n))} /* Michael Somos Nov 11 2006 */
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CROSSREFS
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Cf. A007241, A045478. Convolution square of A007247.
Sequence in context: A106298 A132434 A092714 this_sequence A035811 A004393 A164759
Adjacent sequences: A007264 A007265 A007266 this_sequence A007268 A007269 A007270
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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