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 A386868 #8 Aug 06 2025 08:39:53
%S A386868 1,8,75,760,8030,87036,959623,10710320,120635550,1368461440,
%T A386868 15611831774,178932199152,2058727445320,23764328143220,
%U A386868 275083791201375,3191938947518560,37116092204482550,432393735569959440,5045632228616597290,58965061323736782800,690005032437397594260
%N A386868 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(2*n+2,k) * binomial(2*n-k,n-k).
%F A386868 a(n) = [x^n] (1+x)^(2*n+2)/(1-2*x)^(n+1).
%F A386868 a(n) = [x^n] 1/((1-x)^2 * (1-3*x)^(n+1)).
%F A386868 a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * (n-k+1) * binomial(2*n+2,k).
%F A386868 a(n) = Sum_{k=0..n} 3^k * (n-k+1) * binomial(n+k,k).
%o A386868 (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(2*n+2, k)*binomial(2*n-k, n-k));
%Y A386868 Cf. A385514, A386843.
%K A386868 nonn
%O A386868 0,2
%A A386868 _Seiichi Manyama_, Aug 06 2025