A045820 Theta series of D8 lattice with respect to midpoint of edge.

2, 24, 124, 368, 746, 1288, 2220, 3536, 4964, 6904, 9536, 12112, 15630, 20592, 24588, 29632, 37472, 43296, 50492, 61456, 68724, 79560, 95404, 104352, 118226, 137392, 148636, 167920, 191904, 204712

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A045822.

Programs

Mathematica

terms = 30; List @@ Normal[(1/2)*EllipticTheta[2, 0, z]^2*EllipticTheta[3, 0, z]^6 + O[z]^terms] /. z -> 1 (* Jean-François Alcover, Jul 06 2017 *)
a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, x^(1/2)]^4 EllipticTheta[ 3, 0, x]^4 / (8 Sqrt[x]), {x, 0, n}]; (* Michael Somos, Jul 24 2017 *)

PARI

{a(n) = my(A); if( n<0, 0, A = x * O(x^n); 2 * polcoeff( (eta( x^2 + A)^7 / (eta( x + A)^3 * eta( x^4 + A)^2))^4, n))}; /* Michael Somos, Jul 24 2017 */

Formula

G.f.: (1/2)*(theta_2^2*theta_3^6).

Expansion of q^(-1/2) * 2 * (eta(q^2)^7 / (eta(q)^3 * eta(q^4)^2))^4 in powers of q. - Michael Somos, Jul 24 2017