%I #21 Apr 15 2018 08:59:37
%S 1,72,1800,17568,57096,225072,439200,1210176,1826568,4269096,5626800,
%T 11595744,13931424,26733168,30254400,54917568,58449672,102229776,
%U 106727400,178279200,178482096,295282944,289893600,463416768,445682592
%N Theta series of direct sum of 3 copies of D_4 lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 119.
%D Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 116, equation (4).
%H Seiichi Manyama, <a href="/A008659/b008659.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Da#D4">Index entries for sequences related to D_4 lattice</a>
%F Expansion of (8 * E_6(x^2) - E_6(x)) / 7 in powers of x where E_6() is an Eisenstein series.
%t terms = 25; E6[q_] = 1 - 504 Sum[k^5 q^(2 k)/(1 - q^(2 k)), {k, 1, terms}]; s = (8*E6[q^2] - E6[q])/7 + O[q]^(2 terms); CoefficientList[s, q^2][[1 ;; terms]] (* _Jean-François Alcover_, Jul 04 2017 *)
%o (PARI) {a(n) = if( n<1, n==0, 72 * (sigma( n, 5) - if( n%2, 0, 8 * sigma( n/2, 5))))} /* _Michael Somos_, Jul 16 2004 */
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_