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 A371318 #17 Jun 01 2024 09:48:03
%S A371318 1,2,13,190,4345,135346,5345749,256004974,14416470961,933597699202,
%T A371318 68358972056221,5584583237569150,503607231488672425,
%U A371318 49690178089937051122,5325031693664693833957,615922452708451717999726,76479190243720703567763553
%N A371318 E.g.f. satisfies A(x) = exp(x) + x*A(x)^3.
%F A371318 a(n) = n! * Sum_{k=0..n} (2*k+1)^(n-k-1) * binomial(3*k,k)/(n-k)!.
%F A371318 a(n) ~ sqrt(1 + LambertW(8/27)) * 2^n * n^(n-1) / (3 * exp(n) * LambertW(8/27)^(n + 1/2)). - _Vaclav Kotesovec_, Jun 01 2024
%t A371318 Table[n! Sum[(2 k + 1)^(n - k - 1)*Binomial[3 k, k]/(n - k)!, {k, 0, n}], {n, 0, 20}] (* _Wesley Ivan Hurt_, May 25 2024 *)
%o A371318 (PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(n-k-1)*binomial(3*k, k)/(n-k)!);
%Y A371318 Cf. A000522, A194471, A373324.
%K A371318 nonn
%O A371318 0,2
%A A371318 _Seiichi Manyama_, Mar 18 2024