This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A023918 #28 Nov 11 2021 10:46:04
%S A023918 1,0,0,14,0,42,70,42,0,0,210,0,294,294,210,0,0,504,0,630,882,350,0,0,
%T A023918 1190,0,1470,1148,882,0,0,1680,0,1708,2520,1050,0,0,3150,0,3570,2940,
%U A023918 1750,0,0,3066,0,3864,4774,2100,0,0,6174,0,5740,5124,3570,0,0,6090
%N A023918 Theta series of A*_6 lattice.
%C A023918 Positions of nonzero entries seem to be A047328. - _Andrey Zabolotskiy_, Nov 10 2021
%D A023918 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.
%H A023918 S. Ahlgren, <a href="http://dx.doi.org/10.1090/S0002-9939-99-05181-3">The sixth, eighth, ninth and tenth powers of Ramanujan's theta function</a>, Proc. Amer. Math. Soc., 128 (1999), 1333-1338; F_7(q).
%H A023918 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/As6.html">Home page for this lattice</a>
%F A023918 Expansion of f(-x)^7 / f(-x^7) + 7 * x * f(-x)^3 * f(-x^7)^3 + 7 * x^2 * f(-x^7)^7 / f(-x) in powers of x where f() is a Ramanujan theta function. - _Michael Somos_, Jan 29 2011
%F A023918 a(7*n) = A008446(n). a(7*n + 1) = a(7*n + 2) = a(7*n + 4) = 0. - _Michael Somos_, Jan 29 2011
%e A023918 1 + 14*x^3 + 42*x^5 + 70*x^6 + 42*x^7 + 210*x^10 + 294*x^12 + 294*x^13 + ...
%t A023918 a[n_] := Module[{A, A7}, A = x*O[x]^n; A7 = QPochhammer[x^7 + A]; A = QPochhammer[x + A]; SeriesCoefficient[A^7 / A7 + 7 * x * (A * A7)^3 + 7 * x^2 * A7^7 / A, {x, 0, n}]]; Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Nov 05 2015, adapted from _Michael Somos_'s PARI script *)
%o A023918 (PARI) {a(n) = local(A, A7); if( n<0, 0, A = x * O(x^n); A7 = eta(x^7 + A); A = eta(x + A); polcoeff( A^7 / A7 + 7 * x * (A * A7)^3 + 7 * x^2 * A7^7 / A, n))}; /* _Michael Somos_, Jan 29 2011 */
%Y A023918 Cf. A008446.
%Y A023918 Cf. theta series of lattices A*_0, A*_1, A*_2, A*_3, A*_4...: A000007, A000122, A004016, A004013, A023916, A023917, this sequence, A023919-A023936.
%Y A023918 Cf. A047328.
%K A023918 nonn
%O A023918 0,4
%A A023918 _N. J. A. Sloane_