A383991 Series expansion of the exponential generating function exp(-tridend(-x)) - 1 where tridend(x) = (1 - 3*x - sqrt(1-6*x+x^2)) / (4*x) (A001003).

0, 1, -5, 49, -743, 15421, -407909, 13135165, -498874991, 21838772377, -1082819193029, 59983280191561, -3671752681190615, 246130081055714389, -17932045676505509093, 1410893903131294766101, -119227840965746009631839, 10769985399394862863318705

Offset: 0

Author

Michael De Vlieger, May 16 2025

Keywords

• sign
• easy

Comments

The series -tridend(-x) is the inverse for the substitution of the series trias(x), given by the suspension of the Koszul dual of trias. - Bérénice Delcroix-Oger, May 28 2025

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..348
• 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, triassociative operad "Trias".

Crossrefs

Cf. A003725, A097388, A111884, A112242, A177885, A318215, A383987, A383990, A383992, A383993, A383994, A383995.

Programs

Mathematica

nn = 19; f[x_] := Exp[x] - 1;
Range[0, nn]! * CoefficientList[Series[f[(1 + 3*x - Sqrt[1 + 6*x + x^2])/(4*x)], {x, 0, nn}], x]