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.

1, 1, 2, 5, 14, 44, 152, 569, 2270, 9524, 41576, 187432, 868144, 4117216, 19945408, 98523013, 495521686, 2534420852, 13167361256, 69417635240, 370991119792, 2008036459744, 10997771773888, 60896581502800, 340633178891872

Offset: 0

Author

Paul D. Hanna, May 06 2006

Keywords

• nonn

Comments

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)].

Crossrefs

Cf. A091894.

Programs

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)))}