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%I #28 Dec 12 2023 08:00:40
%S 2,56,252,688,1514,2664,4396,7056,9828,13720,19264,24336,31502,40880,
%T 48780,59584,74592,86688,101308,123088,137844,159016,190764,207648,
%U 235986,275184,297756,335664,384160,410760,453964,520816,553896,601528
%N Theta series of E_8 lattice with respect to midpoint of edge.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 1999, p. 123.
%H Gabriele Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/E8.html">Home page for this lattice</a>.
%F G.f.: (1/2)*(theta_2^2*theta_3^6 + theta_2^6*theta_3^2).
%F a(n) = 2*sigma_3(2n+1). - _Benoit Cloitre_, Apr 12 2003
%F a(n) = 2 * A045823(n). - _Alois P. Heinz_, Mar 21 2021
%F Sum_{k=0..n} a(k) ~ (15*zeta(4)/4) * n^4. - _Amiram Eldar_, Dec 12 2023
%e 2*q^(1/2) + 56*q^(3/2) + 252*q^(5/2) + ...
%t a[n_] := 2 DivisorSigma[3, 2 n + 1]; Table[a[n], {n, 0, 33}] (* _Jean-François Alcover_, Jul 06 2017, after _Benoit Cloitre_ *)
%Y Cf. A001158, A008438, A013662, A045823.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Benoit Cloitre_, Apr 12 2003
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