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 A361599 #11 Mar 17 2023 08:31:47
%S A361599 1,2,11,88,881,10526,145867,2294636,40302593,780263866,16483592171,
%T A361599 376901809472,9265228770481,243493769839958,6808261249400171,
%U A361599 201697053847178836,6308214318127014017,207622266953125336946,7170928402389293540683,259247888385780787392296
%N A361599 Expansion of e.g.f. exp( x/(1-x)^3 ) / (1-x).
%F A361599 a(n) = n! * Sum_{k=0..n} binomial(n+2*k,3*k)/k! = Sum_{k=0..n} (n+2*k)!/(3*k)! * binomial(n,k).
%F A361599 From _Vaclav Kotesovec_, Mar 17 2023: (Start)
%F A361599 a(n) = 2*(2*n - 1)*a(n-1) - (n-1)*(6*n - 11)*a(n-2) + (n-2)*(n-1)*(4*n - 9)*a(n-3) - (n-3)^2*(n-2)*(n-1)*a(n-4).
%F A361599 a(n) ~ 3^(-1/8) * exp(-1/27 - 3^(-5/4)*n^(1/4)/8 + sqrt(n/3)/2 + 4*3^(-3/4)*n^(3/4) - n) * n^(n + 1/8) / 2 * (1 + (34237/69120)*3^(1/4)/n^(1/4)). (End)
%t A361599 Table[n! * Sum[Binomial[n+2*k,3*k]/k!, {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 17 2023 *)
%o A361599 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x)^3)/(1-x)))
%Y A361599 Column k=3 of A361600.
%Y A361599 Cf. A091695.
%K A361599 nonn
%O A361599 0,2
%A A361599 _Seiichi Manyama_, Mar 17 2023