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 A180958 #9 Apr 06 2021 23:09:47
%S A180958 1,1,2,2,2,-1,-8,-25,-57,-114,-202,-322,-447,-496,-271,625,2914,7762,
%T A180958 16834,32063,54760,83319,108375,103726,11110,-282498,-973439,-2366432,
%U A180958 -4869919,-8903455,-14604094,-21135454,-25294718,-19009153,14697432,107405319,311830247,705982670,1386882198,2436851006,3830805953
%N A180958 Diagonal sums of generalized Narayana triangle A180957.
%H A180958 G. C. Greubel, <a href="/A180958/b180958.txt">Table of n, a(n) for n = 0..1000</a>
%H A180958 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-3,-1).
%F A180958 G.f.: ( 1-x-x^2 ) / ( (1+x)*(1-3*x+2*x^2+x^3) ).
%F A180958 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} (-1)^(k-j) * binomial(n-k, j) * binomial(n-k-j, 2*(k-j)).
%t A180958 LinearRecurrence[{2,1,-3,-1}, {1,1,2,2}, 51] (* _G. C. Greubel_, Apr 06 2021 *)
%o A180958 (Magma) I:=[1,1,2,2]; [n le 4 select I[n] else 2*Self(n-1) +Self(n-2) -3*Self(n-3) -Self(n-4): n in [1..51]]; // _G. C. Greubel_, Apr 06 2021
%o A180958 (Sage) [sum( sum( (-1)^(k-j)*binomial(n-k, j)*binomial(n-k-j, 2*(k-j)) for j in (0..n-k)) for k in (0..n//2)) for n in (0..50)] # _G. C. Greubel_, Apr 06 2021
%Y A180958 Cf. A180957.
%K A180958 easy,sign
%O A180958 0,3
%A A180958 _Paul Barry_, Sep 28 2010
%E A180958 Terms a(31) onward added by _G. C. Greubel_, Apr 06 2021