cp's OEIS Frontend

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

%I A195981 #23 Sep 05 2018 09:49:25
%S A195981 1,-1,-1,-1,-2,-4,-10,-25,-66,-178,-490,-1370,-3881,-11113,-32115,
%T A195981 -93542,-274332,-809377,-2400641,-7154066,-21409915,-64317898,
%U A195981 -193886665,-586311736,-1778101466,-5406660260,-16479943037,-50344990445,-154120149335,-472717222756,-1452529814867,-4470733286364,-13782117172530,-42549485082664,-131545321942331
%N A195981 Coefficients of expansion of 1/xi_0(y) (see A195980 for definition).
%C A195981 All the terms after the first are negative.
%H A195981 A. D. Sokal, <a href="http://arxiv.org/abs/1106.1003">The leading root of the partial theta function</a>, arXiv preprint arXiv:1106.1003, 2011.  Adv. Math. 229 (2012), no. 5, 2603-2621.
%t A195981 nmax = 34;
%t A195981 theta0[x_, y_] = Sum[x^n y^(n(n-1)/2), {n, 0, (1/2)(1+Sqrt[1+8nmax]) // Ceiling}];
%t A195981 xi0[y_] = -Sum[a[n] y^n, {n, 0, nmax}];
%t A195981 cc = CoefficientList[theta0[xi0[y], y] + O[y]^(nmax+1) // Normal // Collect[#, y]&, y];
%t A195981 Do[s[n] = Solve[cc[[n+1]] == 0][[1, 1]]; cc = cc /. s[n] , {n, 0, nmax}];
%t A195981 CoefficientList[(-1/xi0[y] /. Array[s, nmax+1, 0]) + O[y]^(nmax+1), y](* _Jean-François Alcover_, Sep 05 2018 *)
%Y A195981 Cf. A195980, A195982, A205999, A206000.
%K A195981 sign
%O A195981 0,5
%A A195981 _N. J. A. Sloane_, Sep 25 2011, Feb 01 2012