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

0,1

Links

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

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

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 *)

Prog

(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 */

Crossrefs

Cf. A045822.

Sequence in context: A179824 A034310 A060817 * A098455 A261475 A078994

Adjacent sequences: A045817 A045818 A045819 * A045821 A045822 A045823

Keyword

nonn

Author

N. J. A. Sloane

Status

approved