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A004007
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Theta series of E_6 lattice.
(Formerly M5349)
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3
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1, 72, 270, 720, 936, 2160, 2214, 3600, 4590, 6552, 5184, 10800, 9360, 12240, 13500, 17712, 14760, 25920, 19710, 26064, 28080, 36000, 25920, 47520, 37638, 43272, 45900, 59040, 46800, 75600, 51840, 69264, 73710, 88560, 62208, 108000, 85176
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 123.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
| Expansion of eta(q)^9/eta(q^3)^3 + 81*q*eta(q^3)^9/eta(q)^3 in powers of q.
Expansion of a(q)^3 +2*c(q)^3 in powers of q where a(),c() are cubic AGM analog functions. - Michael Somos Oct 24 2006
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)^9/eta(x^3+A)^3 +81*x*eta(x^3+A)^9/eta(x+A)^3, n))} /* Michael Somos Oct 24 2006 */
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CROSSREFS
| Cf. A005129 (dual lattice).
Sequence in context: A019507 A158488 A165139 * A173546 A205627 A157909
Adjacent sequences: A004004 A004005 A004006 * A004008 A004009 A004010
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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