A383884 - OEIS

%I #20 Aug 04 2025 07:57:34

%S 1,8,76,776,8236,89528,989080,11055248,124659148,1415338328,

%T 16157960776,185298481904,2133004809976,24631812347696,

%U 285225658980016,3310631101181216,38506555289077516,448698354100917656,5236993294930652776,61212903131657378096,716430640316516361256

%N a(n) = Sum_{k=0..n} 2^k * binomial(2*n+1,k) * binomial(2*n-k,n-k).

%F a(n) = [x^n] (1+2*x)^(2*n+1)/(1-x)^(n+1).

%F a(n) = [x^n] 1/((1-2*x) * (1-3*x)^(n+1)).

%F a(n) = Sum_{k=0..n} 3^k * (-1)^(n-k) * binomial(2*n+1,k).

%F a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(n+k,k).

%o (PARI) a(n) = sum(k=0, n, 2^k*binomial(2*n+1, k)*binomial(2*n-k, n-k));

%Y Cf. A385319.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 04 2025