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 A371116 #9 Mar 11 2024 06:08:19
%S A371116 1,0,0,6,12,20,750,7602,47096,589752,11823930,169812830,2287327812,
%T A371116 46793930196,1061518458182,21163158296490,458344052450160,
%U A371116 12165772611938672,329982890581149426,8764089834124752822,255655700917556204540,8220667673623130347020
%N A371116 E.g.f. satisfies A(x) = 1 + x^2*(exp(x*A(x)) - 1).
%F A371116 a(n) = n! * Sum_{k=0..floor(n/3)} Stirling2(n-2*k,k)/(n-3*k+1)!.
%t A371116 nmax = 20; CoefficientList[Series[1 - x^2 - ProductLog[-E^(x*(1 - x^2))*x^3]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Mar 11 2024 *)
%o A371116 (PARI) a(n) = n!*sum(k=0, n\3, stirling(n-2*k, k, 2)/(n-3*k+1)!);
%Y A371116 Cf. A000272, A371115.
%Y A371116 Cf. A371118.
%K A371116 nonn
%O A371116 0,4
%A A371116 _Seiichi Manyama_, Mar 11 2024