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 A027043 #12 Nov 05 2019 01:00:57
%S A027043 1,6,23,80,285,990,3367,11256,37097,120862,390123,1249728,3978365,
%T A027043 12598350,39718403,124743104,390491505,1218875302,3794984883,
%U A027043 11789335464,36551285573,113120066678,349523991123,1078402178776
%N A027043 a(n) = Sum_{k=0..2n} (k+1) * A027023(n,k).
%H A027043 G. C. Greubel, <a href="/A027043/b027043.txt">Table of n, a(n) for n = 0..1000</a>
%p A027043 T:= proc(n, k) option remember;
%p A027043 if k<3 or k=2*n then 1
%p A027043 else add(T(n-1, k-j), j=1..3)
%p A027043 fi
%p A027043 end:
%p A027043 seq(add((k+1)*T(n,k), k=0..2*n), n=0..30); # _G. C. Greubel_, Nov 04 2019
%t A027043 T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j,3}]]; Table[Sum[(k+1)*T[n,k], {k,0,2*n}], {n,0,30}] (* _G. C. Greubel_, Nov 04 2019 *)
%o A027043 (Sage)
%o A027043 @CachedFunction
%o A027043 def T(n, k):
%o A027043 if (k<3 or k==2*n): return 1
%o A027043 else: return sum(T(n-1, k-j) for j in (1..3))
%o A027043 [sum((k+1)*T(n, k) for k in (0..2*n)) for n in (0..30)] # _G. C. Greubel_, Nov 04 2019
%K A027043 nonn
%O A027043 0,2
%A A027043 _Clark Kimberling_