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 A293493 #24 Jun 08 2024 09:33:28
%S A293493 1,1,1,1,25,121,361,5881,62161,365905,5145841,84831121,812318761,
%T A293493 11450816521,243450591385,3371056121161,51784222133281,
%U A293493 1275605799044641,23531635543402081,410559590525890465,11089633716053137081,256375957896260034841,5161258224477109736521
%N A293493 Expansion of e.g.f. exp(x/(1 - x^3)).
%F A293493 E.g.f.: Product_{k>0} exp(x^(3*k-2)).
%F A293493 a(n) ~ exp(2*sqrt(3*n)/3 - n + 1/6) * n^(n-1/4) / (sqrt(2) * 3^(1/4)). - _Vaclav Kotesovec_, Oct 10 2017
%F A293493 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * (3*k+1)! * a(n-3*k-1). - _Ilya Gutkovskiy_, Feb 24 2022
%F A293493 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k)/(n-3*k)!. - _Seiichi Manyama_, Jun 08 2024
%o A293493 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(1-x^3))))
%o A293493 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(3*k-2)))))
%Y A293493 Cf. A293494.
%K A293493 nonn
%O A293493 0,5
%A A293493 _Seiichi Manyama_, Oct 10 2017