A383577 - OEIS

%I #7 Apr 30 2025 09:11:23

%S 1,1,1,3,13,37,87,241,793,2513,7437,22287,70051,222883,700213,2195139,

%T 6959869,22252933,71201129,227826699,731309001,2356460041,7609531843,

%U 24603325189,79677148959,258535824775,840291483835,2734637778217,8910389207081,29069537051081

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

%C Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - x^2*y^3*z^3).

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

%Y Cf. A383539.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Apr 30 2025