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 A383539 #13 May 30 2025 10:11:46
%S A383539 1,1,1,5,19,49,137,481,1645,5259,17309,59477,203931,693865,2384149,
%T A383539 8277773,28797631,100312525,350891175,1232122535,4335809699,
%U A383539 15287669469,54029225569,191351513905,678850904981,2412164275651,8584573648693,30595269827149
%N A383539 a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,k)^2 * binomial(n-2*k,k).
%C A383539 Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - x^2*y^2*z^3).
%H A383539 Robert Israel, <a href="/A383539/b383539.txt">Table of n, a(n) for n = 0..1758</a>
%p A383539 f:= proc(n) local k; add(binomial(n-k,k)^2 * binomial(n-2*k,k),k=0..n/3) end proc:
%p A383539 map(f, [$0..30]); # _Robert Israel_, May 29 2025
%o A383539 (PARI) a(n) = sum(k=0, n\3, binomial(n-k, k)^2*binomial(n-2*k, k));
%Y A383539 Cf. A383525, A383537.
%Y A383539 Cf. A098479.
%K A383539 nonn
%O A383539 0,4
%A A383539 _Seiichi Manyama_, Apr 29 2025