A371818 - OEIS

%I #11 Apr 07 2024 17:43:43

%S 1,2,6,19,64,224,805,2947,10934,40975,154738,587910,2244681,8605061,

%T 33099767,127687258,493796454,1913755319,7431027611,28902878561,

%U 112585961052,439148770623,1715009647444,6705019714554,26240361155821,102787164654287,402972015656065

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

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

%F a(n) = binomial(2*n, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [1/2-n, -n, 1+n], 27/4). - _Stefano Spezia_, Apr 07 2024

%o (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-2*k, n-3*k));

%Y Cf. A120305, A371819, A371820.

%Y Cf. A000984, A144904.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 06 2024