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 A371816 #12 Aug 07 2025 16:36:16
%S A371816 1,2,10,55,322,1947,12013,75154,474946,3024742,19381045,124797862,
%T A371816 806875421,5234713031,34060165282,222174355575,1452425614146,
%U A371816 9513309908589,62418283102246,410161124310550,2698932409666237,17781425199962255,117281204608676426
%N A371816 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(3*n-3*k-1,n-3*k).
%F A371816 a(n) = [x^n] 1/((1+x^3) * (1-x)^(2*n)).
%F A371816 a(n) = binomial(3*n-1, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [1/3-n, 2/3-n, 1-n], -1). - _Stefano Spezia_, Apr 07 2024
%t A371816 Table[Sum[(-1)^k Binomial[3n-3k-1,n-3k],{k,0,Floor[n/3]}],{n,0,30}] (* _Harvey P. Dale_, Aug 07 2025 *)
%o A371816 (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(3*n-3*k-1, n-3*k));
%Y A371816 Cf. A120305, A165817, A371817.
%Y A371816 Cf. A371770.
%K A371816 nonn
%O A371816 0,2
%A A371816 _Seiichi Manyama_, Apr 06 2024