A383995 Series expansion of the exponential generating function exp(ff6^!(x)) - 1 where ff6^!(x) = x * (1-3*x-x^2+x^3) / (1+3*x+x^2-x^3).

0, 1, -11, 61, -215, -1559, 62941, -1371131, 26310481, -474554735, 7824076741, -98881279859, -176260664711, 87457412423161, -5077434546358355, 234510433823788501, -10016559114085864799, 413333665704129673249, -16704968283664639137899, 660340818239784197391325

Offset: 0

Author

Michael De Vlieger, May 16 2025

Keywords

• sign

Comments

The series ff6^!(x) is the inverse for the substitution of the series ff6(x) (given by A231690), given by the suspension of the Koszul dual of FF6. - Bérénice Delcroix-Oger, May 28 2025

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..393
• 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 "FF6".

Crossrefs

Cf. A003725, A097388, A111884, A112242, A177885, A318215, A383989, A383990, A383991, A383992, A383993, A383994.

Programs

Mathematica

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