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A383988
Series expansion of the exponential generating function -postLie(1-exp(x)) where postLie(x) = -log((1 + sqrt(1-4*x)) / 2) (given by A006963).
5
0, 1, -2, 12, -110, 1380, -22022, 426972, -9747950, 256176660, -7617417302, 252851339532, -9268406209790, 371843710214340, -16206868062692582, 762569209601624892, -38525315595630383630, 2079964082064837282420, -119513562475103977951862
OFFSET
0,3
COMMENTS
The series -postLie(-x) is the inverse for the substitution of the series comTrias(x), given by the suspension of the Koszul dual of comTrias. - Bérénice Delcroix-Oger, May 28 2025
LINKS
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, commutative triassociative operad "ComTrias".
MATHEMATICA
nn = 18; f[x_] := Log[(1 + Sqrt[1 + 4*x])/2];
Range[0, nn]! * CoefficientList[Series[f[-(1 - Exp[x])], {x, 0, nn}], x]
CROSSREFS
Cf. A002050, A006531, A084099, A097388, A101851, A114285, A225883, A383985, A383986, A383987, A383989. Composition of -A006963(-x) and exp(x)-1.
Sequence in context: A158832 A372158 A264916 * A296644 A235860 A317208
KEYWORD
sign,easy
AUTHOR
Michael De Vlieger, May 16 2025
STATUS
approved