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 A368323 #12 Aug 18 2025 13:15:13
%S A368323 1,6,48,516,7212,125436,2616348,63662556,1770359772,55384885596,
%T A368323 1925211581148,73613650011996,3070625126631132,138757783222353756,
%U A368323 6752624341715261148,352087859568330751836,19582053567267458627292,1157162515572965014445916
%N A368323 Expansion of e.g.f. exp(3*x) / (4 - 3*exp(x)).
%F A368323 a(n) = 3^n + 3 * Sum_{k=1..n} binomial(n,k) * a(n-k).
%F A368323 a(n) = (64/27)*A032033(n) - (1/3)*(2^n + 4/3 + (16/9)*0^n).
%t A368323 With[{nn=20},CoefficientList[Series[Exp[3x]/(4-3Exp[x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 18 2025 *)
%o A368323 (PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
%o A368323 a(n, m=3, t=3) = my(u=1+1/t); u^m*b(n, t)-(1/t)*sum(j=0, m-1, u^j*(m-1-j)^n);
%Y A368323 Cf. A032033, A201354, A368322, A368324.
%K A368323 nonn
%O A368323 0,2
%A A368323 _Seiichi Manyama_, Dec 21 2023