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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
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
Sequence in context: A127713 A354076 A151256 * A208126 A370646 A208452
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 02 2012, Feb 03 2012
STATUS
approved

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Last modified April 16 19:21 EDT 2024. Contains 371754 sequences. (Running on oeis4.)