A118398 Eigenvector of the triangle defined by T(n,k) = 2^k*C(n,2*k) for 0<=k<=[n/2], n>=0.

1, 1, 3, 7, 25, 81, 267, 855, 2865, 9889, 34963, 124455, 443977, 1583089, 5640603, 20071287, 71341665, 253483329, 901388067, 3211744839, 11477295225, 41157734289, 148140201003, 535151245719, 1939739625873, 7051722637281

Offset: 0

Author

Paul D. Hanna, May 08 2006

Keywords

• eigen
• nonn

Comments

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

Examples

			a(7) = Sum_{k=0..[7/2]} 2^k*C(7,2*k)*a(k) =
1*(1) + 42*(1) + 140*(3) + 56*(7) = 855.
		

Crossrefs

Cf. A118397 (self-convolution).

Programs

PARI

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

Formula

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).