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 A368534 #18 May 14 2025 19:08:15
%S A368534 0,1,5,24,146,1215,13431,186816,3130436,61291125,1371742105,
%T A368534 34522712136,964626945558,29621465864627,991330604373851,
%U A368534 35906022352657920,1399219698628043016,58367293868445147657,2594796705962971336125,122463905297217627859000
%N A368534 a(n) = Sum_{k=1..n} binomial(k+1,2) * n^(n-k).
%F A368534 a(n) = [x^n] x/((1-n*x) * (1-x)^3).
%F A368534 a(n) = n * (2*n^(n+1) - n^3 - n^2 + n - 1)/(2 * (n-1)^3) for n > 1.
%t A368534 Table[Sum[Binomial[k+1,2]n^(n-k),{k,n}],{n,0,20}] (* _Harvey P. Dale_, May 14 2025 *)
%o A368534 (PARI) a(n) = sum(k=1, n, binomial(k+1, 2)*n^(n-k));
%Y A368534 Cf. A062805, A368535.
%Y A368534 Cf. A002662, A052150, A052161.
%Y A368534 Cf. A023037, A062806, A068475.
%K A368534 nonn,easy
%O A368534 0,3
%A A368534 _Seiichi Manyama_, Dec 29 2023