A383993 Series expansion of the exponential generating function exp(tridup^!(x)) - 1 where tridup^!(x) = x / ((1+x) * (1+2*x)).

0, 1, -5, 25, -119, 301, 5611, -171275, 3574705, -68597639, 1282415131, -23479249199, 409082338105, -6146707844315, 46462772999371, 2072826643602541, -160983324879816479, 8004468391727017585, -352443295329194182085, 14817357881274444545161

Offset: 0

Author

Michael De Vlieger, May 16 2025

Keywords

• sign
• easy

Comments

The series tridup^!(x) is the inverse for the substitution of the series tridup(x) (given by A001003), given by the suspension of the Koszul dual of tridup. - Bérénice Delcroix-Oger, May 28 2025

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..404
• 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, triduplicial operad "TriDup".

Crossrefs

Cf. A002050, A003725, A097388, A111884, A112242, A177885, A318215, A383990, A383991, A383992, A383994, A383995.

Programs

Mathematica

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