A383989 Series expansion of the exponential generating function ff6^!(exp(x)-1) where ff6^!(x) = x * (1-3*x-x^2+x^3) / (1+3*x+x^2-x^3).

0, 1, -11, 61, -467, 4381, -49091, 643021, -9615827, 161844541, -3026079971, 62243374381, -1396619164787, 33949401567901, -888725861445251, 24926889744928141, -745755560487363347, 23705772035082494461, -797875590555470224931, 28346366547928396344301

Offset: 0

Author

Michael De Vlieger, May 16 2025

Keywords

• sign
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..407
• Bérénice Delcroix-Oger and Clément Dupont, Lie-operads and operadic modules from poset cohomology, arXiv:2505.06094 [math.CO], 2025. See p. 28, Table 2, operad "FF6".

Crossrefs

Cf. A002050, A006531, A084099, A101851, A114285, A225883, A383985, A383986, A383987, A383988, A383995.

Programs

Mathematica

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