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A118929 a(n) = Sum_{k=0..[n/2]} 2^(n-2*k-1)*C(n-1,2*k)*C(2*k,k)/(k+1)*a(k), with a(0)=1. 0


%S 1,1,2,5,14,44,152,569,2270,9524,41576,187432,868144,4117216,19945408,

%T 98523013,495521686,2534420852,13167361256,69417635240,370991119792,

%U 2008036459744,10997771773888,60896581502800,340633178891872

%N a(n) = Sum_{k=0..[n/2]} 2^(n-2*k-1)*C(n-1,2*k)*C(2*k,k)/(k+1)*a(k), with a(0)=1.

%C Invariant column vector V under matrix product A091894*V = V: a(n) = Sum_{k=0,[n/2]} A091894(n,k)*a(k), where A091894(n,k) = number of Dyck paths of semilength n, having k ddu's [here u=(1,1) and d=(1,-1)].

%o (PARI) {a(n)=if(n==0,1,sum(k=0,n\2,2^(n-2*k-1)*binomial(n-1,2*k)*binomial(2*k,k)/(k+1)*a(k)))}

%Y Cf. A091894.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 06 2006

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Last modified August 4 19:54 EDT 2020. Contains 336202 sequences. (Running on oeis4.)