|
%I #23 Jul 07 2023 14:57:14
%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>
%F a(0) = 1; a(n) = -(n-1)! * Sum_{k=1..n} A186690(k) * a(n-k)/(n-k)!. - _Seiichi Manyama_, Jul 07 2023
%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, A186690.
%Y Cf. A015682, A015683, A015684, A015685, A015687, A015690, A015691, A015693, A015694, A015695, A015696, A015697.
%K sign
%O 0,3
%A _N. J. A. Sloane_
|
