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A125094 Eigensequence of A061554 regarded as a triangle: a(n) = Sum_{k=0..n-1} A061554(n-1,k)*a(k) with a(0)=1.

%I A125094 #3 Mar 30 2012 18:37:01
%S A125094 1,1,2,5,13,36,104,313,977,3152,10486,35880,126039,453725,1671322,
%T A125094 6291148,24170312,94680426,377788108,1534169595,6335718925,
%U A125094 26589240583,113323479393,490203781505,2150975413846,9569147610181,43140286838567
%N A125094 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 A125094 a(n) = Sum_{k=0..n-1} a(k)*C(n-1, floor[n/2 - (-1)^(n-k-1)*(k+1)/2] ).
%e A125094 a(4) = 3*(1) + 3*(1) + 1*(2) + 1*(5) = 13.
%e A125094 a(5) = 6*(1) + 4*(1) + 4*(2) + 1*(5) + 1*(13) = 36.
%e A125094 a(6) = 10*(1) + 10*(1) + 5*(2) + 5*(5) + 1*(13) + 1*(36) = 104.
%e A125094 Triangle version of A061554 begins:
%e A125094 1;
%e A125094 1, 1;
%e A125094 2, 1, 1;
%e A125094 3, 3, 1, 1;
%e A125094 6, 4, 4, 1, 1;
%e A125094 10, 10, 5, 5, 1, 1; ...
%o A125094 (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 A125094 Cf. A061554.
%K A125094 nonn
%O A125094 0,3
%A A125094 _Paul D. Hanna_, Nov 20 2006