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%I #15 Oct 16 2018 07:27:37
%S 1,84,574,1288,3444,4424,9240,11088,18494,19740,34440,31304,52808,
%T 52248,74048,71120,110964,94864,145222,132888,181384,163856,249480,
%U 201040,295960,264684,346696,314272,454608,352520,518336,452256,591934,517216
%N Theta series of D_7 lattice.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 118.
%H Seiichi Manyama, <a href="/A008429/b008429.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: (theta_3(q^(1/2))^7 + theta_4(q^(1/2))^7)/2.
%e 1 + 84*q^2 + 574*q^4 + 1288*q^6 + 3444*q^8 + ...
%t terms = 34; s = 1/2 (EllipticTheta[3, 0, q]^7 + EllipticTheta[4, 0, q]^7) + O[q]^(2 terms); CoefficientList[s, q^2] (* _Jean-François Alcover_, Jul 07 2017 *)
%o (PARI) {a(n)=if(n<0, 0, n*=2; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n))^7, n))} /* _Michael Somos_, Nov 03 2006 */
%Y A008451(2n) = a(n).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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