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 A383993 #12 May 28 2025 16:38:18
%S A383993 0,1,-5,25,-119,301,5611,-171275,3574705,-68597639,1282415131,
%T A383993 -23479249199,409082338105,-6146707844315,46462772999371,
%U A383993 2072826643602541,-160983324879816479,8004468391727017585,-352443295329194182085,14817357881274444545161
%N A383993 Series expansion of the exponential generating function exp(tridup^!(x)) - 1 where tridup^!(x) = x / ((1+x) * (1+2*x)).
%C A383993 The series tridup^!(x) is the inverse for the substitution of the series tridup(x) (given by A001003), given by the suspension of the Koszul dual of tridup. - _Bérénice Delcroix-Oger_, May 28 2025
%H A383993 Michael De Vlieger, <a href="/A383993/b383993.txt">Table of n, a(n) for n = 0..404</a>
%H A383993 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, triduplicial operad "TriDup".
%t A383993 nn = 19; f[x_] := Exp[x] - 1;
%t A383993 Range[0, nn]! * CoefficientList[Series[f[x/((1 + x)*(1 + 2*x))], {x, 0, nn}], x]
%Y A383993 Cf. A002050, A003725, A097388, A111884, A112242, A177885, A318215, A383990, A383991, A383992, A383994, A383995.
%K A383993 sign,easy
%O A383993 0,3
%A A383993 _Michael De Vlieger_, May 16 2025