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 A346754 #15 Dec 15 2023 08:29:51
%S A346754 0,0,0,1,4,10,30,175,1176,7364,50520,425205,4010380,39433966,
%T A346754 414654604,4793188855,59834495280,789420239560,11016095913456,
%U A346754 163423065359529,2565467553034740,42320595474149650,732058678770177220,13275485607004016011
%N A346754 Expansion of e.g.f. -log( 1 - x^3 * exp(x) / 3! ).
%F A346754 a(0) = 0; a(n) = binomial(n,3) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * binomial(n-k,3) * k * a(k).
%F A346754 a(n) ~ (n-1)! / (3*LambertW(2^(1/3)/3^(2/3)))^n. - _Vaclav Kotesovec_, Aug 08 2021
%F A346754 a(n) = n! * Sum_{k=1..floor(n/3)} k^(n-3*k-1)/(6^k * (n-3*k)!). - _Seiichi Manyama_, Dec 14 2023
%t A346754 nmax = 23; CoefficientList[Series[-Log[1 - x^3 Exp[x]/3!], {x, 0, nmax}], x] Range[0, nmax]!
%t A346754 a[0] = 0; a[n_] := a[n] = Binomial[n, 3] + (1/n) Sum[Binomial[n, k] Binomial[n - k, 3] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 23}]
%Y A346754 Cf. A000292, A009444, A145453, A292954, A305990, A346751, A346753, A346755.
%K A346754 nonn
%O A346754 0,5
%A A346754 _Ilya Gutkovskiy_, Aug 01 2021