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A008435 Theta series of {D_7}^{+} packing. 1


%S 1,0,0,0,0,0,0,64,84,0,0,0,0,0,0,448,574,0,0,0,0,0,0,1344,1288,0,0,0,

%T 0,0,0,2688,3444,0,0,0,0,0,0,4928,4424,0,0,0,0,0,0,8064,9240,0,0,0,0,

%U 0,0,11200,11088,0,0,0

%N Theta series of {D_7}^{+} packing.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

%H Seiichi Manyama, <a href="/A008435/b008435.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>

%F From _Seiichi Manyama_, Oct 21 2018: (Start)

%F Expansion of (theta_2(q)^7 + theta_3(q)^7 + theta_4(q)^7)/2 in powers of q^(1/4).

%F Expansion of (Sum_{k=-inf..inf} q^((k+1/2)^2))^7 + (Sum_{k=-inf..inf} q^(k^2))^7 + (Sum_{k=-inf..inf} (-1)^k * q^(k^2))^7 in powers of q^(1/4). (End)

%e G.f.: 1 + 64*q^(7/4) + 84*q^2 + 448*q^(15/4) + 574*q^4 + ... .

%Y Cf. A008429.

%K nonn,easy

%O 0,8

%A _N. J. A. Sloane_

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)