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A045819
Theta series of E_8 lattice with respect to midpoint of edge.
1
2, 56, 252, 688, 1514, 2664, 4396, 7056, 9828, 13720, 19264, 24336, 31502, 40880, 48780, 59584, 74592, 86688, 101308, 123088, 137844, 159016, 190764, 207648, 235986, 275184, 297756, 335664, 384160, 410760, 453964, 520816, 553896, 601528
OFFSET
0,1
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 1999, p. 123.
LINKS
Gabriele Nebe and N. J. A. Sloane, Home page for this lattice.
FORMULA
G.f.: (1/2)*(theta_2^2*theta_3^6 + theta_2^6*theta_3^2).
a(n) = 2*sigma_3(2n+1). - Benoit Cloitre, Apr 12 2003
a(n) = 2 * A045823(n). - Alois P. Heinz, Mar 21 2021
Sum_{k=0..n} a(k) ~ (15*zeta(4)/4) * n^4. - Amiram Eldar, Dec 12 2023
EXAMPLE
2*q^(1/2) + 56*q^(3/2) + 252*q^(5/2) + ...
MATHEMATICA
a[n_] := 2 DivisorSigma[3, 2 n + 1]; Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Jul 06 2017, after Benoit Cloitre *)
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from Benoit Cloitre, Apr 12 2003
STATUS
approved