This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383991 #25 May 28 2025 09:19:19
%S A383991 0,1,-5,49,-743,15421,-407909,13135165,-498874991,21838772377,
%T A383991 -1082819193029,59983280191561,-3671752681190615,246130081055714389,
%U A383991 -17932045676505509093,1410893903131294766101,-119227840965746009631839,10769985399394862863318705
%N A383991 Series expansion of the exponential generating function exp(-tridend(-x)) - 1 where tridend(x) = (1 - 3*x - sqrt(1-6*x+x^2)) / (4*x) (A001003).
%C A383991 The series -tridend(-x) is the inverse for the substitution of the series trias(x), given by the suspension of the Koszul dual of trias. - _Bérénice Delcroix-Oger_, May 28 2025
%H A383991 Michael De Vlieger, <a href="/A383991/b383991.txt">Table of n, a(n) for n = 0..348</a>
%H A383991 Bérénice Delcroix-Oger and Clément Dupont, <a href="https://arxiv.org/abs/2505.06094">Lie-operads and operadic modules from poset cohomology</a>, arXiv:2505.06094 [math.CO], 2025. See p. 32, Table 3, triassociative operad "Trias".
%t A383991 nn = 19; f[x_] := Exp[x] - 1;
%t A383991 Range[0, nn]! * CoefficientList[Series[f[(1 + 3*x - Sqrt[1 + 6*x + x^2])/(4*x)], {x, 0, nn}], x]
%Y A383991 Cf. A003725, A097388, A111884, A112242, A177885, A318215, A383987, A383990, A383992, A383993, A383994, A383995.
%K A383991 sign,easy
%O A383991 0,3
%A A383991 _Michael De Vlieger_, May 16 2025