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%I #17 Nov 11 2023 08:49:42
%S 1,56,126,576,756,1512,2072,4032,4158,5544,7560,12096,11592,13664,
%T 16704,24192,24948,27216,31878,44352,39816,41832,55944,72576,66584,
%U 67536,76104,100800,99792,101304,116928,145728,133182,126504,160272,205632,177660,176456,205128,249984,249480,234360
%N Nonzero coefficients in theta series of {E_7}* lattice.
%C In the Eichler and Zagier reference this is e_4(A014601(n)), n >= 0, (p. 141), where e_4 is obtained from e_{4,1}(n,r), eq. (7), p. 22, depending only on 4*n-r^2 >= 0 (for integers n and r), i.e. on A014601(n), n >= 0 (with a new notation for n). - _Wolfdieter Lang_, Jan 08 2016
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 125.
%D M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhäuser, 1985, p. 141.
%H N. Elkies and B. H. Gross, <a href="http://dx.doi.org/10.2140/pjm.1997.181.147">Embeddings into the integral octonions, Olga Taussky-Todd: in memoriam</a>, Pacific J. Math. 1997, Special Issue, 147-158.
%o (PARI) f(n) = local(A); if( n<0, 0, A = sum(k=1, sqrtint(n), 2 * x^k^2, 1 + x * O(x^n)); polcoeff( A^3 * (A^4 + 7 * subst(A, x, -x)^4) / 8, n)); \\ A003781
%o lista(nn) = select(x->(x>0), vector(nn, k, f(k-1))); \\ _Michel Marcus_, Nov 11 2023
%Y Cf. A003781.
%K nonn
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Michel Marcus_, Nov 11 2023