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A205999 Inverse Euler transform of A195980. 3
1, 1, 2, 4, 10, 23, 61, 157, 426, 1163, 3253, 9172, 26236, 75634, 220021, 644305, 1898977, 5626720, 16754652, 50104781, 150427938, 453214878, 1369857943, 4152559458, 12621816592, 38459047705, 117453028937, 359455509767, 1102239999454, 3386090204843, 10419804578693, 32115276396739, 99131502581481, 306422345148052, 948423189115351 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequence is conjectured to be positive, nondecreasing and strictly convex.

LINKS

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

N. J. A. Sloane, Transforms

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.

MATHEMATICA

nmax = 35;

theta0[x_, y_] = Sum[x^n y^(n (n-1)/2), {n, 0, (1/2) (1 + Sqrt[1 + 8 nmax]) // Ceiling}];

xi0[y_] = -Sum[b[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}];

A195980 = Table[b[n] /. s[n], {n, 1, nmax}];

mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];

EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i b[[i]] - Sum[c[[d]] b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i) Sum[mob[i, d] c[[d]], {d, 1, i}]]]; Return[a]];

EULERi[A195980] (* Jean-Fran├žois Alcover, Oct 04 2018 *)

CROSSREFS

Cf. A195980, A206000.

Sequence in context: A032171 A127713 A151256 * A208126 A208452 A208453

Adjacent sequences:  A205996 A205997 A205998 * A206000 A206001 A206002

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 02 2012, Feb 03 2012

STATUS

approved

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Last modified February 26 09:05 EST 2020. Contains 332277 sequences. (Running on oeis4.)