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 A351282 #13 Feb 07 2022 21:44:39
%S A351282 1,3,12,48,201,885,4116,20298,106365,592455,3503532,21946620,
%T A351282 145210305,1011726417,7400390052,56668826118,453116188821,
%U A351282 3774297532467,32682069679548,293632972911048,2732593851548985,26299137526992525,261387306941467188,2679392140776188706
%N A351282 a(n) = Sum_{k=0..n} 3^k * k^(n-k).
%H A351282 Seiichi Manyama, <a href="/A351282/b351282.txt">Table of n, a(n) for n = 0..572</a>
%F A351282 a(n) ~ sqrt(2*Pi/(1 + LambertW(exp(1)*n/3))) * n^(n + 1/2) * exp(n/LambertW(exp(1)*n/3) - n) / LambertW(exp(1)*n/3)^(n + 1/2).
%F A351282 G.f.: Sum_{k>=0} 3^k * x^k / (1 - k*x). - _Ilya Gutkovskiy_, Feb 06 2022
%t A351282 Join[{1}, Table[Sum[3^k*k^(n-k), {k, 0, n}], {n, 1, 25}]]
%o A351282 (PARI) a(n) = sum(k=0, n, 3^k*k^(n-k)); \\ _Michel Marcus_, Feb 06 2022
%Y A351282 Cf. A003101, A351279.
%K A351282 nonn
%O A351282 0,2
%A A351282 _Vaclav Kotesovec_, Feb 06 2022