This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118398 #3 Mar 30 2012 18:36:57
%S A118398 1,1,3,7,25,81,267,855,2865,9889,34963,124455,443977,1583089,5640603,
%T A118398 20071287,71341665,253483329,901388067,3211744839,11477295225,
%U A118398 41157734289,148140201003,535151245719,1939739625873,7051722637281
%N A118398 Eigenvector of the triangle defined by T(n,k) = 2^k*C(n,2*k) for 0<=k<=[n/2], n>=0.
%C A118398 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 A118398 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 A118398 a(7) = Sum_{k=0..[7/2]} 2^k*C(7,2*k)*a(k) =
%e A118398 1*(1) + 42*(1) + 140*(3) + 56*(7) = 855.
%o A118398 (PARI) a(n)=if(n==0,1,sum(k=0,n\2,2^k*binomial(n,2*k)*a(k)))
%Y A118398 Cf. A118397 (self-convolution).
%K A118398 eigen,nonn
%O A118398 0,3
%A A118398 _Paul D. Hanna_, May 08 2006