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 A383326 #18 Aug 04 2025 07:53:01
%S A383326 1,7,71,799,9439,114687,1419263,17791487,225172991,2870945791,
%T A383326 36819740671,474470776831,6138443497471,79681448443903,
%U A383326 1037278449106943,13536444411412479,177030837540093951,2319618918724403199,30444928900076666879,400189735705069486079,5267487129636270243839
%N A383326 a(n) = Sum_{k=0..n} binomial(3*n+1,k) * binomial(3*n-k,n-k).
%F A383326 a(n) = [x^n] (1+x)^(3*n+1)/(1-x)^(2*n+1).
%F A383326 a(n) = [x^n] 1/((1-x) * (1-2*x)^(2*n+1)).
%F A383326 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(3*n+1,k).
%F A383326 a(n) = Sum_{k=0..n} 2^k * binomial(2*n+k,k).
%o A383326 (PARI) a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(3*n-k, n-k));
%Y A383326 Cf. A178792, A383716.
%Y A383326 Cf. A370097.
%K A383326 nonn
%O A383326 0,2
%A A383326 _Seiichi Manyama_, Aug 04 2025