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A045820 Theta series of D8 lattice with respect to midpoint of edge. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 19 06:03 EST 2019. Contains 329310 sequences. (Running on oeis4.)