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A023918
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Theta series of A*_6 lattice.
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0
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1, 0, 0, 14, 0, 42, 70, 42, 0, 0, 210, 0, 294, 294, 210, 0, 0, 504, 0, 630, 882, 350, 0, 0, 1190, 0, 1470, 1148, 882, 0, 0, 1680, 0, 1708, 2520, 1050, 0, 0, 3150, 0, 3570
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc., 128 (1999), 1333-1338; F_7(q).
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.
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LINKS
| G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
| Expansion of f(-x)^7 / f(-x^7) + 7 * x * f(-x)^3 * f(-x^7)^3 + 7 * x^2 * f(-x^7)^7 / f(-x) in powers of x where f() is a Ramanujan theta function. - Michael Somos Jan 29 2011
a(7*n) = A008446(n). a(7*n + 1) = a(7*n + 2) = a(7*n + 4) = 0. - Michael Somos Jan 29 2011
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EXAMPLE
| 1 + 14*x^3 + 42*x^5 + 70*x^6 + 42*x^7 + 210*x^10 + 294*x^12 + 294*x^13 + ...
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PROG
| (PARI) {a(n) = local(A, A7); if( n<0, 0, A = x * O(x^n); A7 = eta(x^7 + A); A = eta(x + A); polcoeff( A^7 / A7 + 7 * x * (A * A7)^3 + 7 * x^2 * A7^7 / A, n))}; /* Michael Somos Jan 29 2011 */
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CROSSREFS
| Sequence in context: A181170 A002337 A008423 * A062785 A161384 A198806
Adjacent sequences: A023915 A023916 A023917 * A023919 A023920 A023921
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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