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A195981 Coefficients of expansion of 1/xi_0(y) (see A195980 for definition). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

All the terms after the first are negative.

LINKS

Table of n, a(n) for n=0..34.

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.

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 *)

CROSSREFS

Cf. A195980, A195982, A205999, A206000.

Sequence in context: A230555 A189912 A268321 * A124500 A220872 A317876

Adjacent sequences:  A195978 A195979 A195980 * A195982 A195983 A195984

KEYWORD

sign

AUTHOR

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

STATUS

approved

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Last modified February 25 20:52 EST 2020. Contains 332258 sequences. (Running on oeis4.)