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 A351735 #13 Aug 30 2025 11:39:13
%S A351735 1,0,6,27,324,4050,64962,1224720,26776656,665390376,18529576200,
%T A351735 571602980520,19349098690248,713092338026640,28422424039182768,
%U A351735 1218246132898693080,55876497505161154560,2730710993688989519040,141654212475516155694528
%N A351735 Expansion of e.g.f. 1/(1 - 3 * x)^x.
%F A351735 a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-k) * |Stirling1(n-k,k)|/(n-k)!.
%F A351735 a(n) ~ sqrt(2*Pi) * 3^n * n^(n - 1/6) / (Gamma(1/3) * exp(n)). - _Vaclav Kotesovec_, Aug 30 2025
%o A351735 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x)^x))
%o A351735 (PARI) a(n) = n!*sum(k=0, n\2, 3^(n-k)*abs(stirling(n-k, k, 1))/(n-k)!);
%Y A351735 Cf. A053490, A053491.
%K A351735 nonn,changed
%O A351735 0,3
%A A351735 _Seiichi Manyama_, May 20 2022