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 A195255 #7 Oct 10 2020 08:25:38
%S A195255 1,3,12,51,234,1179,6624,41931,300078,2420307,21841812,218595267,
%T A195255 2405079378,28862546859,375217892136,5253064838811,78796015628886,
%U A195255 1260736379202339,21432518833860252,385785340171746003,7329921466749958458,146598429345459522363
%N A195255 O.g.f.: Sum_{n>=0} 3*(n+3)^(n-1)*x^n/(1+n*x)^n.
%C A195255 Compare the g.f. to: W(x)^3 = Sum_{n>=0} 3*(n+3)^(n-1)*x^n/n! where W(x) = LambertW(-x)/(-x).
%C A195255 Compare to a g.f. of A000522: Sum_{n>=0} (n+1)^(n-1)*x^n/(1+n*x)^n, which generates the total number of arrangements of a set with n elements.
%F A195255 a(n) = (n-1)!*Sum_{k=1..n} 3^k/(k-1)! for n>0, with a(0)=1.
%F A195255 a(n) ~ 3*exp(3) * (n-1)!. - _Vaclav Kotesovec_, Oct 10 2020
%e A195255 O.g.f.: A(x) = 1 + 3*x + 12*x^2 + 51*x^3 + 234*x^4 + 1179*x^5 +...
%e A195255 where
%e A195255 A(x) = 1 + 3*x/(1+x) + 3*5*x^2/(1+2*x)^2 + 3*6^2*x^3/(1+3*x)^3 + 3*7^3*x^4/(1+4*x)^4 +..
%o A195255 (PARI) {a(n)=polcoeff(sum(m=0,n,3*(m+3)^(m-1)*x^m/(1+m*x+x*O(x^n))^m),n)}
%o A195255 (PARI) {a(n)=if(n==0,1,(n-1)!*sum(k=1,n,3^k/(k-1)!))}
%Y A195255 Cf. A000522, A195254, A195256, A195257.
%K A195255 nonn
%O A195255 0,2
%A A195255 _Paul D. Hanna_, Sep 13 2011