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%I #26 Aug 03 2024 16:44:52
%S 1,0,0,0,0,0,0,0,144,256,0,0,0,0,0,0,2034,2304,0,0,0,0,0,0,7392,9216,
%T 0,0,0,0,0,0,22608,23808,0,0,0,0,0,0,44640,50688,0,0,0,0,0,0,93984,
%U 96768,0,0,0,0,0,0,141120
%N Theta series of {D_9}^{+} packing.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.
%H Seiichi Manyama, <a href="/A008436/b008436.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)^9 + theta_3(q)^9 + theta_4(q)^9)/2 in powers of q^(1/4).
%F Expansion of (Sum_{k=-oo..oo} q^((k+1/2)^2))^9 + (Sum_{k=-oo..oo} q^(k^2))^9 + (Sum_{k=-oo..oo} (-1)^k * q^(k^2))^9 in powers of q^(1/4). (End)
%e G.f.: 1 + 144*q^2 + 256*q^(9/4) + 2034*q^4 + 2304*q^(17/4) + ... .
%Y Cf. A000122 (theta_3(q)), A002448 (theta_4(q)), A008431.
%K nonn,easy
%O 0,9
%A _N. J. A. Sloane_