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 A351734 #13 Apr 02 2025 18:10:54
%S A351734 1,0,6,9,120,555,5148,39711,378528,3715011,39838260,452684463,
%T A351734 5463506304,69553644771,930940368036,13054086036855,191222363275968,
%U A351734 2918620069099395,46309955947643124,762335523354333855,12995722456718984160,229045407317491457763
%N A351734 Expansion of e.g.f. exp( 3 * x * (exp(x) - 1) ).
%F A351734 a(n) = n! * Sum_{k=0..floor(n/2)} 3^k * Stirling2(n-k,k)/(n-k)!.
%t A351734 With[{nn=30},CoefficientList[Series[Exp[3x (Exp[x]-1)],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 02 2025 *)
%o A351734 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(3*x*(exp(x)-1))))
%o A351734 (PARI) a(n) = n!*sum(k=0, n\2, 3^k*stirling(n-k, k, 2)/(n-k)!);
%Y A351734 Cf. A052506, A351733.
%Y A351734 Cf. A053490, A351737.
%K A351734 nonn
%O A351734 0,3
%A A351734 _Seiichi Manyama_, May 20 2022