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 A081197 #10 Sep 08 2022 08:45:09
%S A081197 0,0,0,1,4,13,44,162,643,2724,12259,58423,293902,1555743,8640526,
%T A081197 50222288,304792741,1927313470,12673784445,86517541197,612134881624,
%U A081197 4482215342305,33919417267456,264951302794510,2133720505175351
%N A081197 Diagonal sums of A081130.
%H A081197 G. C. Greubel, <a href="/A081197/b081197.txt">Table of n, a(n) for n = 0..500</a>
%F A081197 a(n) = Sum_{k=1..n-2} k^(n-k-2)*binomial(n-k, 2).
%F A081197 a(n) = Sum_{k=0..n-1} (n-k)^(k-2)*binomial(k, 2). - _G. C. Greubel_, May 15 2021
%p A081197 A081197 := proc(n)
%p A081197 add(k^(n-k-2)*binomial(n-k,2), k=1..n-2) ;
%p A081197 end proc: # _R. J. Mathar_, Feb 13 2015
%t A081197 Table[Sum[k^(n-k-2)*Binomial[n-k, 2], {k,n-2}], {n,0,30}] (* _G. C. Greubel_, May 15 2021 *)
%o A081197 (Magma) [n lt 3 select 0 else (&+[j^(n-j-2)*Binomial(n-j,2): j in [1..n-2]]): n in [0..30]]; // _G. C. Greubel_, May 15 2021
%o A081197 (Sage) [sum( (n-k)^(k-2)*binomial(k,2) for k in (0..n-1) ) for n in (0..30)] # _G. C. Greubel_, May 15 2021
%Y A081197 Cf. A081130.
%K A081197 easy,nonn
%O A081197 0,5
%A A081197 _Paul Barry_, Mar 11 2003
%E A081197 Terms corrected by _G. C. Greubel_, May 15 2021