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 A371819 #10 Apr 07 2024 17:43:46
%S A371819 1,3,10,34,118,417,1497,5447,20047,74493,279054,1052467,3992204,
%T A371819 15216662,58239175,223688159,861769598,3328779906,12887832493,
%U A371819 49998248601,194315972151,756406944446,2948649839743,11509316352548,44976030493706,175942932935325
%N A371819 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-k+1,n-3*k).
%F A371819 a(n) = [x^n] 1/(((1-x)^2+x^3) * (1-x)^n).
%F A371819 a(n) = binomial(1+2*n, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [-1-2*n, 1+n/2, (3+n)/2], -27/4). - _Stefano Spezia_, Apr 07 2024
%o A371819 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-k+1, n-3*k));
%Y A371819 Cf. A001700, A120305, A371818, A371820.
%Y A371819 Cf. A371773.
%K A371819 nonn
%O A371819 0,2
%A A371819 _Seiichi Manyama_, Apr 06 2024