A015680 Expansion of e.g.f. theta_3^(-1/2).

1, -1, 3, -15, 81, -585, 4995, -46935, 499905, -6109425, 79791075, -1138096575, 17774982225, -294439570425, 5240530570275, -100050497922375, 2002010508122625, -42495475420022625, 954152290944727875

Offset

0,3

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..443

Formula

a(0) = 1; a(n) = -(n-1)! * Sum_{k=1..n} A186690(k) * a(n-k)/(n-k)!. - Seiichi Manyama, Jul 07 2023

Example

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 + ... .

Mathematica

nmax = 25; CoefficientList[Series[EllipticTheta[3, 0, x]^(-1/2), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2018 *)

Crossrefs

Cf. A000122 (theta_3), A015664, A186690.

Cf. A015682, A015683, A015684, A015685, A015687, A015690, A015691, A015693, A015694, A015695, A015696, A015697.

Sequence in context: A264225 A343975 A255676 * A371516 A084208 A059271

Adjacent sequences: A015677 A015678 A015679 * A015681 A015682 A015683

Keyword

sign

Author

N. J. A. Sloane

Status

approved