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 A351934 #22 Jun 08 2024 08:51:07
%S A351934 1,1,1,1,5,21,61,281,1961,10585,59641,509521,4086061,29792621,
%T A351934 288051765,2997900361,27857436881,302238265841,3759751338481,
%U A351934 43054257392545,526471319508181,7463835257515141,101755979383832621,1404876681654178041,22115830210157954425
%N A351934 Expansion of e.g.f. exp(x / (1 - x^3/6)).
%F A351934 a(n) = Sum_{k=0..floor((n-1)/3)} (3*k+1)!/6^k * binomial(n-1,3*k) * a(n-1-3*k) for n > 3.
%F A351934 a(n) ~ n^(n - 1/4) / (2^(n/3 + 5/12) * 3^(n/3 + 1/6) * exp(n - 2^(7/6) * 3^(-1/3) * sqrt(n) - 6^(-2/3))). - _Vaclav Kotesovec_, Mar 03 2022
%F A351934 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k)/(6^k * (n-3*k)!). - _Seiichi Manyama_, Jun 08 2024
%t A351934 m = 24; Range[0, m]! * CoefficientList[Series[Exp[x/(1 - x^3/6)], {x, 0, m}], x] (* _Amiram Eldar_, Feb 26 2022 *)
%o A351934 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x^3/6))))
%o A351934 (PARI) a(n) = if(n<4, 1, sum(k=0, (n-1)\3, (3*k+1)!/6^k*binomial(n-1, 3*k)*a(n-1-3*k)));
%Y A351934 Cf. A000262, A351933, A351935, A351936.
%Y A351934 Cf. A293493.
%K A351934 nonn
%O A351934 0,5
%A A351934 _Seiichi Manyama_, Feb 26 2022