A195981 Coefficients of expansion of 1/xi_0(y) (see A195980 for definition).

1, -1, -1, -1, -2, -4, -10, -25, -66, -178, -490, -1370, -3881, -11113, -32115, -93542, -274332, -809377, -2400641, -7154066, -21409915, -64317898, -193886665, -586311736, -1778101466, -5406660260, -16479943037, -50344990445, -154120149335, -472717222756, -1452529814867, -4470733286364, -13782117172530, -42549485082664, -131545321942331

Offset: 0

Author

N. J. A. Sloane, Sep 25 2011, Feb 01 2012

Keywords

• sign

Comments

All the terms after the first are negative.

Links

• A. D. Sokal, The leading root of the partial theta function, arXiv preprint arXiv:1106.1003, 2011. Adv. Math. 229 (2012), no. 5, 2603-2621.

Crossrefs

Cf. A195980, A195982, A205999, A206000.

Programs

Mathematica

nmax = 34;
theta0[x_, y_] = Sum[x^n y^(n(n-1)/2), {n, 0, (1/2)(1+Sqrt[1+8nmax]) // Ceiling}];
xi0[y_] = -Sum[a[n] y^n, {n, 0, nmax}];
cc = CoefficientList[theta0[xi0[y], y] + O[y]^(nmax+1) // Normal // Collect[#, y]&, y];
Do[s[n] = Solve[cc[[n+1]] == 0][[1, 1]]; cc = cc /. s[n] , {n, 0, nmax}];
CoefficientList[(-1/xi0[y] /. Array[s, nmax+1, 0]) + O[y]^(nmax+1), y](* Jean-François Alcover, Sep 05 2018 *)