A383986 Expansion of the exponential generating function sqrt(4*exp(x) - exp(2*x) - 2) - 1.

0, 1, -1, 1, -13, 61, -601, 5881, -73333, 1021861, -16334401, 290146561, -5707536253, 122821558861, -2873553719401, 72586328036041, -1969306486088773, 57106504958139061, -1762735601974347601, 57705363524117482321, -1996916624448159410893

Offset: 0

Author

Michael De Vlieger, May 16 2025

Keywords

• sign
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..409
• 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 "NAC_2".

Crossrefs

Cf. A002050, A006531, A084099, A101851, A114285, A182037, A225883, A383985, A383987, A383988, A383989.

Programs

Mathematica

nn = 20; f[x_] := -1 + Sqrt[1 + 2 x - x^2];
Range[0, nn]! * CoefficientList[Series[f[-(1 - Exp[x])], {x, 0, nn}], x]