cp's OEIS Frontend

A118397 Eigenvector of triangle A105070, where A105070(n,k) = 2^k*C(n+1,2*k+1) for 0<=k<=[n/2], n>=0.

%I A118397 #3 Mar 30 2012 18:36:57
%S A118397 1,2,7,20,73,254,895,3080,10801,38426,138775,504284,1838137,6705494,
%T A118397 24464719,89204624,324981985,1183034546,4305313447,15672486692,
%U A118397 57100841641,208309692974,761141694367,2785955603096,10215141094417
%N A118397 Eigenvector of triangle A105070, where A105070(n,k) = 2^k*C(n+1,2*k+1) for 0<=k<=[n/2], n>=0.
%C A118397 Self-convolution of A118398, which is also an eigenvector of the triangle defined by T(n,k) = 2^k*C(n,2*k).
%F A118397 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 A118397 a(7) = Sum_{k=0..[7/2]} A105070(7,k)*a(k) =
%e A118397 8*(1) + 112*(2) + 224*(7) + 64*(20) = 3080.
%o A118397 (PARI) a(n)=if(n==0,1,sum(k=0,n\2,2^k*binomial(n+1,2*k+1)*a(k)))
%Y A118397 Cf. A105070 (triangle), A118398 (A(x)^(1/2)).
%K A118397 eigen,nonn
%O A118397 0,2
%A A118397 _Paul D. Hanna_, May 08 2006