%I #3 Mar 30 2012 18:37:01

%S 1,1,2,5,13,36,104,313,977,3152,10486,35880,126039,453725,1671322,

%T 6291148,24170312,94680426,377788108,1534169595,6335718925,

%U 26589240583,113323479393,490203781505,2150975413846,9569147610181,43140286838567

%N Eigensequence of A061554 regarded as a triangle: a(n) = Sum_{k=0..n-1} A061554(n-1,k)*a(k) with a(0)=1.

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

%e a(4) = 3*(1) + 3*(1) + 1*(2) + 1*(5) = 13.

%e a(5) = 6*(1) + 4*(1) + 4*(2) + 1*(5) + 1*(13) = 36.

%e a(6) = 10*(1) + 10*(1) + 5*(2) + 5*(5) + 1*(13) + 1*(36) = 104.

%e Triangle version of A061554 begins:

%e 1;

%e 1, 1;

%e 2, 1, 1;

%e 3, 3, 1, 1;

%e 6, 4, 4, 1, 1;

%e 10, 10, 5, 5, 1, 1; ...

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

%Y Cf. A061554.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 20 2006