A383536 - OEIS

%I #7 Apr 29 2025 08:54:48

%S 1,1,10,33,301,1468,12006,70945,548218,3588451,27033942,187329660,

%T 1398372925,10015968040,74666604910,545706810657,4076875022533,

%U 30186038308420,226302738440884,1690539173230083,12722171581599588,95650154853862786,722460110890588300

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

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

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

%Y Cf. A112019.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 29 2025