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A195980 Coefficients of expansion of "leading root" xi_0(y) of the partial theta function Sum_{n=0..oo} x^n y^{n(n-1)/2}. 4
1, 1, 2, 4, 9, 21, 52, 133, 351, 948, 2610, 7298, 20672, 59192, 171059, 498275, 1461437, 4312300, 12792342, 38128354, 114126797, 342914278, 1033914760, 3127154610, 9485523742, 28848101993, 87948036401, 268724650863, 822791384597, 2524113596369, 7757247543181, 23880003051017, 73627904162143, 227347168628991, 702970760225573, 2176459051318522 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sokal (2011) shows that all the terms are positive.

LINKS

Table of n, a(n) for n=0..35.

Ramón Flores, Juan González-Meneses, On the growth of Artin--Tits monoids and the partial theta function, arXiv:1808.03066 [math.GR], 2018.

Thomas Prellberg, The combinatorics of the leading root of the partial theta function, arXiv:1210.0095 [math.CO], 2012.

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

A. D. Sokal, The first 6999 terms

MATHEMATICA

nmax = 35;

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}];

Table[a[n] /. s[n], {n, 0, nmax}] (* Jean-François Alcover, Sep 05 2018 *)

CROSSREFS

Cf. A195981, A195982, A205999, A206000.

Sequence in context: A148071 A000636 A204352 * A136753 A289666 A084261

Adjacent sequences:  A195977 A195978 A195979 * A195981 A195982 A195983

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)