A045820 - OEIS

%I #19 Jul 25 2017 04:11:56

%S 2,24,124,368,746,1288,2220,3536,4964,6904,9536,12112,15630,20592,

%T 24588,29632,37472,43296,50492,61456,68724,79560,95404,104352,118226,

%U 137392,148636,167920,191904,204712

%N Theta series of D8 lattice with respect to midpoint of edge.

%H Vincenzo Librandi, <a href="/A045820/b045820.txt">Table of n, a(n) for n = 0..1000</a>

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

%F 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

%t 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 *)

%t 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 *)

%o (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 */

%Y Cf. A045822.

%K nonn

%O 0,1

%A _N. J. A. Sloane_