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 A383884 #20 Aug 04 2025 07:57:34
%S A383884 1,8,76,776,8236,89528,989080,11055248,124659148,1415338328,
%T A383884 16157960776,185298481904,2133004809976,24631812347696,
%U A383884 285225658980016,3310631101181216,38506555289077516,448698354100917656,5236993294930652776,61212903131657378096,716430640316516361256
%N A383884 a(n) = Sum_{k=0..n} 2^k * binomial(2*n+1,k) * binomial(2*n-k,n-k).
%F A383884 a(n) = [x^n] (1+2*x)^(2*n+1)/(1-x)^(n+1).
%F A383884 a(n) = [x^n] 1/((1-2*x) * (1-3*x)^(n+1)).
%F A383884 a(n) = Sum_{k=0..n} 3^k * (-1)^(n-k) * binomial(2*n+1,k).
%F A383884 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(n+k,k).
%o A383884 (PARI) a(n) = sum(k=0, n, 2^k*binomial(2*n+1, k)*binomial(2*n-k, n-k));
%Y A383884 Cf. A385319.
%K A383884 nonn
%O A383884 0,2
%A A383884 _Seiichi Manyama_, Aug 04 2025