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 A362087 #9 Apr 08 2023 11:11:45
%S A362087 1,1,7,37,215,1271,7651,46614,286599,1774630,11050897,69134572,
%T A362087 434174819,2735565574,17283825370,109466361512,694764983463,
%U A362087 4417771590123,28137563496298,179478199605550,1146342590242465,7330598365285470,46928753892901140
%N A362087 a(n) = Sum_{k=0..n} (-1)^k * binomial(-n,k) * binomial(2*k,n-k).
%F A362087 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(2*k,n-k).
%F A362087 a(n) = [x^n] 1/(1 - x*(1+x)^2)^n.
%t A362087 Table[Sum[Binomial[n + k - 1, k]*Binomial[2*k, n-k], {k, 0, n}], {n, 0, 25}] (* _Vaclav Kotesovec_, Apr 08 2023 *)
%o A362087 (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(2*k, n-k));
%Y A362087 Column k=2 of A362078.
%Y A362087 Cf. A362084.
%K A362087 nonn
%O A362087 0,3
%A A362087 _Seiichi Manyama_, Apr 08 2023