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 A349970 #19 Dec 08 2021 06:49:26
%S A349970 1,1,3,9,31,125,579,3009,17255,108005,731883,5331625,41501135,
%T A349970 343405709,3007557523,27775308049,269603741111,2742598070709,
%U A349970 29164361115067,323444222468089,3733412864370975,44767318872513885,556707323098632547,7168524182698345313
%N A349970 a(n) = Sum_{k=0..n} (2*k)^(n-k).
%H A349970 Seiichi Manyama, <a href="/A349970/b349970.txt">Table of n, a(n) for n = 0..500</a>
%F A349970 G.f.: Sum_{k>=0} x^k/(1 - 2*k * x).
%F A349970 a(n) ~ sqrt(Pi) * (2*n/LambertW(2*exp(1)*n))^(1/2 + n - n/LambertW(2*exp(1)*n)) / sqrt(1 + LambertW(2*exp(1)*n)). - _Vaclav Kotesovec_, Dec 07 2021
%t A349970 a[n_] := Sum[If[k == n == 0, 1, (2*k)^(n - k)], {k, 0, n}]; Array[a, 24, 0] (* _Amiram Eldar_, Dec 07 2021 *)
%o A349970 (PARI) a(n) = sum(k=0, n, (2*k)^(n-k));
%o A349970 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-2*k*x)))
%Y A349970 Cf. A349963, A349969.
%K A349970 nonn
%O A349970 0,3
%A A349970 _Seiichi Manyama_, Dec 07 2021