A118398 - OEIS

%I #3 Mar 30 2012 18:36:57

%S 1,1,3,7,25,81,267,855,2865,9889,34963,124455,443977,1583089,5640603,

%T 20071287,71341665,253483329,901388067,3211744839,11477295225,

%U 41157734289,148140201003,535151245719,1939739625873,7051722637281

%N Eigenvector of the triangle defined by T(n,k) = 2^k*C(n,2*k) for 0<=k<=[n/2], n>=0.

%C Self-convolution square-root of A118397, which is also an eigenvector of triangle A105070(n,k) = 2^k*C(n+1,2*k+1).

%F Eigenvector: a(n) = Sum_{k=0..[n/2]} 2^k*C(n,2*k)*a(k) for n>=0, with a(0)=1. O.g.f. A(x) satisfies: A(x/(1+x))/(1+x) = A(2*x^2).

%e a(7) = Sum_{k=0..[7/2]} 2^k*C(7,2*k)*a(k) =

%e 1*(1) + 42*(1) + 140*(3) + 56*(7) = 855.

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

%Y Cf. A118397 (self-convolution).

%K eigen,nonn

%O 0,3

%A _Paul D. Hanna_, May 08 2006