A383994 Series expansion of the exponential generating function exp(wnp^!(x)) - 1 where wnp^!(x) = log(1+x) - x^2/(1+x).

0, 1, -2, 0, 12, -60, 240, -840, 1680, 15120, -332640, 4656960, -59209920, 735134400, -9098369280, 112345833600, -1365274310400, 15746578848000, -155630893017600, 762963647846400, 22567767443020800, -1126188650069683200, 35900904478389350400

Offset: 0

Author

Michael De Vlieger, May 16 2025

Keywords

• sign

Comments

The series wnp^!(x) is the inverse for the substitution of the series wnp(x) (corresponding to A048172), given by the suspension of the Koszul dual of the WithoutNPosets operad. - Bérénice Delcroix-Oger, May 28 2025

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..451
• Bérénice Delcroix-Oger and Clément Dupont, Lie-operads and operadic modules from poset cohomology, arXiv:2505.06094 [math.CO], 2025. See p. 32, Table 3, operad without n posets "WNP".

Crossrefs

Cf. A003725, A084099, A097388, A111884, A112242, A177885, A318215, A383990, A383991, A383992, A383993, A383995.

Programs

Mathematica

nn = 22; f[x_] := Exp[x] - 1;
Range[0, nn]! * CoefficientList[Series[f[Log[1 + x] - x^2/(1 + x)], {x, 0, nn}], x]