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 A386899 #15 Aug 07 2025 08:34:58
%S A386899 1,16,339,7840,189295,4689216,118155156,3013479744,77557234095,
%T A386899 2010176842960,52394920516939,1371957494204544,36062378503314436,
%U A386899 950984592573500800,25147592297769065400,666594977732384307840,17706778517771676847215,471217399398861925667760
%N A386899 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(3*n+1,k) * binomial(2*n-k,n-k).
%F A386899 a(n) = [x^n] (1+3*x)^(3*n+1)/(1-2*x)^(n+1).
%F A386899 a(n) = [x^n] 1/((1-3*x) * (1-5*x))^(n+1).
%F A386899 a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(3*n+1,k) * binomial(2*n-k,n-k).
%F A386899 a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(n+k,k) * binomial(2*n-k,n-k).
%F A386899 a(n) = 2^n*binomial(2*n, n)*hypergeom([-1-3*n, -n], [-2*n], -3/2). - _Stefano Spezia_, Aug 07 2025
%o A386899 (PARI) a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(3*n+1, k)*binomial(2*n-k, n-k));
%Y A386899 Cf. A386830, A386900.
%Y A386899 Cf. A244038.
%K A386899 nonn
%O A386899 0,2
%A A386899 _Seiichi Manyama_, Aug 07 2025