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 A355471 #13 Feb 16 2023 09:49:38
%S A355471 1,1,2,10,77,808,11257,196072,4136897,103755904,3034193921,
%T A355471 101901347944,3885951145969,166605168800704,7961498177012993,
%U A355471 420976047757358776,24475992585921169553,1556007778666449968128,107625967130820901112833
%N A355471 Expansion of Sum_{k>=0} (x/(1 - k^2 * x))^k.
%F A355471 a(n) = Sum_{k=1..n} k^(2*(n-k)) * binomial(n-1,k-1) for n > 0.
%t A355471 Flatten[{1, Table[Sum[Binomial[n-1,k-1] * k^(2*(n-k)), {k,1,n}], {n,1,20}]}] (* _Vaclav Kotesovec_, Feb 16 2023 *)
%o A355471 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k^2*x))^k))
%o A355471 (PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(2*(n-k))*binomial(n-1, k-1)));
%Y A355471 Cf. A080108, A135746, A234568, A355463, A355472.
%K A355471 nonn
%O A355471 0,3
%A A355471 _Seiichi Manyama_, Jul 03 2022