A205999 Inverse Euler transform of A195980.

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

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-François Alcover, Oct 04 2018 *)

Crossrefs

Cf. A195980, A206000.

Sequence in context: A127713 A354076 A151256 * A208126 A370646 A208452

Adjacent sequences: A205996 A205997 A205998 * A206000 A206001 A206002

Keyword

nonn

Author

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

Status

approved