A015665
Expansion of e.g.f. theta_3^(3/2).
Original entry on oeis.org
1, 3, 3, -3, 81, 315, -765, 4725, 16065, 1091475, 10843875, -65956275, 770425425, 5892561675, -6512831325, 213901813125, 47691165146625, 1318815779155875, -7354191439720125, 223312383805636125, 2055628831852220625
Offset: 0
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.
-
nmax = 25; CoefficientList[Series[EllipticTheta[3, 0, x]^(3/2), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2018 *)
A015680
Expansion of e.g.f. theta_3^(-1/2).
Original entry on oeis.org
1, -1, 3, -15, 81, -585, 4995, -46935, 499905, -6109425, 79791075, -1138096575, 17774982225, -294439570425, 5240530570275, -100050497922375, 2002010508122625, -42495475420022625, 954152290944727875
Offset: 0
theta_3(q)^(-1/2) = 1 - q + 3/2 * q^2 - 5/2 * q^3 + 27/8 *q^4 - 39/8 * q^5 + ... = 1 - q + 3/2! * q^2 - 15/3! * q^3 + 81/4! * q^4 - 585/5! * q^5 + ... .
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.
Cf.
A015682,
A015683,
A015684,
A015685,
A015687,
A015690,
A015691,
A015693,
A015694,
A015695,
A015696,
A015697.
-
nmax = 25; CoefficientList[Series[EllipticTheta[3, 0, x]^(-1/2), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2018 *)
Showing 1-2 of 2 results.