A319308
Expansion of theta_4(q)^20 in powers of q = exp(Pi i t).
Original entry on oeis.org
1, -40, 760, -9120, 77560, -497648, 2508000, -10232640, 34729720, -100906760, 259114704, -606957280, 1327461600, -2738111280, 5341699520, -9915552192, 17701924600, -30615844560, 51294999960, -83279292960, 131880275664, -204949382400, 312126610080, -464844224960, 680432137440
Offset: 0
A319309
Expansion of theta_4(q)^24 in powers of q = exp(Pi i t).
Original entry on oeis.org
1, -48, 1104, -16192, 170064, -1362336, 8662720, -44981376, 195082320, -721175536, 2319457632, -6631997376, 17231109824, -41469483552, 93703589760, -200343312768, 407488018512, -793229226336, 1487286966928, -2697825744960, 4744779429216, -8110465650176
Offset: 0
A319310
Expansion of theta_4(q)^28 in powers of q = exp(Pi i t).
Original entry on oeis.org
1, -56, 1512, -26208, 327656, -3147984, 24189984, -152867520, 811401192, -3681079640, 14500933104, -50376047904, 156797510688, -444306558864, 1163495873088, -2851049839680, 6597606440936, -14512424533488, 30505974273096, -61591664700384, 119983597365744, -226303038736128
Offset: 0
A008409
Theta series of 16-dimensional Barnes-Wall lattice.
Original entry on oeis.org
1, 0, 4320, 61440, 522720, 2211840, 8960640, 23224320, 67154400, 135168000, 319809600, 550195200, 1147643520, 1771683840, 3371915520, 4826603520, 8593797600, 11585617920, 19590534240, 25239859200, 40979580480, 50877235200
Offset: 0
1 + 4320*q^4 + 61440*q^6 + 522720*q^8 + 2211840*q^10 + 8960640*q^12 + ...
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 130, p. 131 Equation (132).
- Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)
- N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
- G. Nebe and N. J. A. Sloane, Home page for this lattice
- Index entries for sequences related to Barnes-Wall lattices
- Eric Weisstein's World of Mathematics, Theta Series
- Eric Weisstein's World of Mathematics, Barnes-Wall Lattice
-
f[q_] := 1/2*(EllipticTheta[2, 0, q]^16 + EllipticTheta[3, 0, q]^16 + EllipticTheta[4, 0, q]^16 + 30*EllipticTheta[2, 0, q]^8*EllipticTheta[3, 0, q]^8); Series[f[q], {q, 0, 21}] // CoefficientList[#, q]& (* Jean-François Alcover, May 15 2013 *)
-
{a(n) = local(A1, A2) ; if( n<0, 0, A1 = eta(x + x * O(x^n))^8; A2 = eta(x^2 + x * O(x^n))^8; polcoeff( (A1^6 + 32 * x * A1^3 * A2^3 + 4096 * x^2 * A2^6) / ( A1 * A2 )^2, n))} /* Michael Somos, Nov 29 2007 */
Showing 1-4 of 4 results.