A004532 - OEIS

%I #21 Aug 01 2024 23:14:37

%S 1,0,0,0,180,512,0,0,3380,5120,0,0,16320,23040,0,0,52020,66560,0,0,

%T 129064,153600,0,0,262080,313344,0,0,489600,565760,0,0,840500,936960,

%U 0,0,1330420,1497600,0,0,2050344,2263040

%N Theta series of {D_10}^{+} lattice.

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

%H Seiichi Manyama, <a href="/A004532/b004532.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)^10 + theta_3(q)^10 + theta_4(q)^10)/2 in powers of q^(1/2).

%F Expansion of (Sum_{k=-inf..inf} q^((k+1/2)^2))^10 + (Sum_{k=-inf..inf} q^(k^2))^10 + (Sum_{k=-inf..inf} (-1)^k * q^(k^2))^10 in powers of q^(1/2). (End)

%Y Cf. A000122 (theta_3(q)), A002448 (theta_4(q)), A008432.

%K nonn

%O 0,5

%A _N. J. A. Sloane_