Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #3 Mar 30 2012 18:36:57
%S 1,2,7,20,73,254,895,3080,10801,38426,138775,504284,1838137,6705494,
%T 24464719,89204624,324981985,1183034546,4305313447,15672486692,
%U 57100841641,208309692974,761141694367,2785955603096,10215141094417
%N Eigenvector of triangle A105070, where A105070(n,k) = 2^k*C(n+1,2*k+1) for 0<=k<=[n/2], n>=0.
%C Self-convolution of A118398, which is also an eigenvector of the triangle defined by T(n,k) = 2^k*C(n,2*k).
%F Eigenvector: a(n) = Sum_{k=0..[n/2]} 2^k*C(n+1,2*k+1)*a(k) for n>=0, with a(0)=1. O.g.f. A(x) satisfies: A(x/(1+x))/(1+x)^2 = A(2*x^2).
%e a(7) = Sum_{k=0..[7/2]} A105070(7,k)*a(k) =
%e 8*(1) + 112*(2) + 224*(7) + 64*(20) = 3080.
%o (PARI) a(n)=if(n==0,1,sum(k=0,n\2,2^k*binomial(n+1,2*k+1)*a(k)))
%Y Cf. A105070 (triangle), A118398 (A(x)^(1/2)).
%K eigen,nonn
%O 0,2
%A _Paul D. Hanna_, May 08 2006