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 A346890 #19 May 13 2022 18:23:15
%S A346890 1,0,0,0,1,5,15,35,140,1386,12810,92730,589545,4234945,41832791,
%T A346890 483334215,5401798220,57262207380,626438655900,7740130412796,
%U A346890 107197808258745,1546730804858085,22360919412385015,329241486278715395,5121840342205301946
%N A346890 Expansion of e.g.f. 1 / (1 - x^4 * exp(x) / 4!).
%H A346890 Seiichi Manyama, <a href="/A346890/b346890.txt">Table of n, a(n) for n = 0..482</a>
%F A346890 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * binomial(k,4) * a(n-k).
%F A346890 a(n) ~ n! / ((1 + LambertW(3^(1/4)/2^(5/4))) * 4^(n + 1) * LambertW(3^(1/4)/2^(5/4))^n). - _Vaclav Kotesovec_, Aug 08 2021
%F A346890 a(n) = n! * Sum_{k=0..floor(n/4)} k^(n-4*k)/(24^k * (n-4*k)!). - _Seiichi Manyama_, May 13 2022
%t A346890 nmax = 24; CoefficientList[Series[1/(1 - x^4 Exp[x]/4!), {x, 0, nmax}], x] Range[0, nmax]!
%t A346890 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Binomial[k, 4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
%o A346890 (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-x^4*exp(x)/4!))) \\ _Michel Marcus_, Aug 06 2021
%o A346890 (PARI) a(n) = n!*sum(k=0, n\4, k^(n-4*k)/(24^k*(n-4*k)!)); \\ _Seiichi Manyama_, May 13 2022
%Y A346890 Column k=4 of A351703.
%Y A346890 Cf. A006153, A346888, A346889, A346893.
%Y A346890 Cf. A000332, A145454.
%K A346890 nonn
%O A346890 0,6
%A A346890 _Ilya Gutkovskiy_, Aug 06 2021