A383985 Series expansion of the exponential generating function LambertW(1-exp(x)), see A000169.

0, 1, -1, 4, -23, 181, -1812, 22037, -315569, 5201602, -97009833, 2019669961, -46432870222, 1168383075471, -31939474693297, 942565598033196, -29866348653695203, 1011335905644178273, -36446897413531401020, 1392821757824071815641, -56259101478392975833333

Offset: 0

Author

Michael De Vlieger, May 16 2025

Keywords

• sign
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..200
• 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, permutative commutative operad "Perm/Com2".

Crossrefs

Cf. A002050, A006531, A084099, A101851, A114285, A177885, A225883, A383986, A383987, A383988, A383989.

Composition of A000169 with signs and 1-exp(x).

Programs

Mathematica

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