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A015680 Expansion of e.g.f. theta_3^(-1/2). 3

%I

%S 1,-1,3,-15,81,-585,4995,-46935,499905,-6109425,79791075,-1138096575,

%T 17774982225,-294439570425,5240530570275,-100050497922375,

%U 2002010508122625,-42495475420022625,954152290944727875

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

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

%H Seiichi Manyama, <a href="/A015680/b015680.txt">Table of n, a(n) for n = 0..443</a>

%e 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 + ... .

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

%Y Cf. A000122 (theta_3), A015664.

%K sign,changed

%O 0,3

%A _N. J. A. Sloane_

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Last modified January 25 12:40 EST 2022. Contains 350572 sequences. (Running on oeis4.)