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A015680 Expansion of e.g.f. theta_3^(-1/2). 3
1, -1, 3, -15, 81, -585, 4995, -46935, 499905, -6109425, 79791075, -1138096575, 17774982225, -294439570425, 5240530570275, -100050497922375, 2002010508122625, -42495475420022625, 954152290944727875 (list; graph; refs; listen; history; text; internal format)
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

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.

Sequence in context: A264225 A343975 A255676 * A084208 A059271 A345885

Adjacent sequences:  A015677 A015678 A015679 * A015681 A015682 A015683

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 26 17:52 EST 2021. Contains 349343 sequences. (Running on oeis4.)