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 A349883 #18 Dec 06 2021 03:10:07
%S A349883 1,1,5,60,1242,41241,2033683,141318208,13262986788,1624337451945,
%T A349883 252725477615989,48858277079478156,11523986801592238046,
%U A349883 3265676705193282018577,1097336766468309067029991,432291795385094609190468384,197690320046319097006619353352
%N A349883 Expansion of Sum_{k>=0} (k * x)^k/(1 - k^3 * x).
%H A349883 Seiichi Manyama, <a href="/A349883/b349883.txt">Table of n, a(n) for n = 0..227</a>
%F A349883 a(n) = Sum_{k=0..n} k^(3*n-2*k).
%F A349883 a(n) ~ sqrt(Pi) * (3/2)^(1/2 + 3*n - 3*n/LambertW(3*exp(1)*n/2)) * (n/LambertW(3*exp(1)*n/2))^(1/2 + 3*n - 3*n/LambertW(3*exp(1)*n/2)) / sqrt(1 + LambertW(3*exp(1)*n/2)). - _Vaclav Kotesovec_, Dec 04 2021
%t A349883 a[n_] := Sum[If[k == 3*n - 2*k == 0, 1, k^(3*n - 2*k)], {k, 0, n}]; Array[a, 17, 0] (* _Amiram Eldar_, Dec 04 2021 *)
%o A349883 (PARI) a(n, t=3) = sum(k=0, n, k^(t*(n-k)+k));
%o A349883 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^3*x)))
%Y A349883 Cf. A031971, A349836, A349901.
%K A349883 nonn
%O A349883 0,3
%A A349883 _Seiichi Manyama_, Dec 03 2021