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 A386866 #11 Sep 02 2025 19:30:25
%S A386866 1,9,132,2197,38649,701292,12979360,243541725,4616122851,88173726337,
%T A386866 1694554311888,32728267058604,634701136059532,12351249029265816,
%U A386866 241061116082196072,4716751239386395885,92494719333403946583,1817328001770278062299,35768122814759119268788
%N A386866 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(3*n+2,k) * binomial(3*n-k-1,n-k).
%F A386866 a(n) = [x^n] (1+x)^(3*n+2)/(1-2*x)^(2*n).
%F A386866 a(n) = [x^n] 1/((1-x)^3 * (1-3*x)^(2*n)).
%F A386866 a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * binomial(3*n+2,k) * binomial(n-k+2,n-k).
%F A386866 a(n) = Sum_{k=0..n} 3^k * binomial(2*n+k-1,k) * binomial(n-k+2,n-k).
%t A386866 Table[Sum[2^(n-k) Binomial[3n+2,k]Binomial[3n-k-1,n-k],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Sep 02 2025 *)
%o A386866 (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(3*n+2, k)*binomial(3*n-k-1, n-k));
%Y A386866 Cf. A384950, A386863.
%Y A386866 Cf. A386836.
%K A386866 nonn,changed
%O A386866 0,2
%A A386866 _Seiichi Manyama_, Aug 06 2025