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 A346889 #19 May 13 2022 18:22:39
%S A346889 1,0,0,1,4,10,40,315,2296,15204,117720,1127445,11531740,120909646,
%T A346889 1370809804,17111895255,227853866800,3182209445640,47003318806896,
%U A346889 737325061500009,12187616610231540,210930852047426770,3821604062633503300,72479758506840597451
%N A346889 Expansion of e.g.f. 1 / (1 - x^3 * exp(x) / 3!).
%H A346889 Seiichi Manyama, <a href="/A346889/b346889.txt">Table of n, a(n) for n = 0..464</a>
%F A346889 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * binomial(k,3) * a(n-k).
%F A346889 a(n) ~ n! / ((1 + LambertW(2^(1/3)/3^(2/3))) * 3^(n+1) * LambertW(2^(1/3)/3^(2/3))^n). - _Vaclav Kotesovec_, Aug 08 2021
%F A346889 a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k)/(6^k * (n-3*k)!). - _Seiichi Manyama_, May 13 2022
%t A346889 nmax = 23; CoefficientList[Series[1/(1 - x^3 Exp[x]/3!), {x, 0, nmax}], x] Range[0, nmax]!
%t A346889 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Binomial[k, 3] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]
%o A346889 (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-x^3*exp(x)/3!))) \\ _Michel Marcus_, Aug 06 2021
%o A346889 (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)/(6^k*(n-3*k)!)); \\ _Seiichi Manyama_, May 13 2022
%Y A346889 Column k=3 of A351703.
%Y A346889 Cf. A006153, A346888, A346890, A346893.
%Y A346889 Cf. A000292, A145453, A353999.
%K A346889 nonn
%O A346889 0,5
%A A346889 _Ilya Gutkovskiy_, Aug 06 2021