A378554 - OEIS

%I #14 Nov 30 2024 09:49:54

%S 1,1,7,28,171,846,4942,26580,153363,856900,4939682,28140476,162676878,

%T 936947116,5436375532,31526252208,183571246659,1069552636950,

%U 6247183319938,36524006501180,213899020967786,1253905101529080,7359775341696180,43237184121401400

%N a(n) = Sum_{k=0..n} 4^(n-k) * binomial(n+k-1,k) * binomial(k/2,n-k).

%F a(n) = [x^n] 1/(1 - x*(1 + 4*x)^(1/2))^n.

%t a[n_]:=SeriesCoefficient[1/(1 - x*(1 + 4*x)^(1/2))^n,{x,0,n}]; Array[a,24,0] (* _Stefano Spezia_, Nov 30 2024 *)

%o (PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(n+k-1, k)*binomial(k/2, n-k));

%Y Cf. A213684, A378555.

%Y Cf. A372125.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 30 2024