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

1, 2, 7, 20, 73, 254, 895, 3080, 10801, 38426, 138775, 504284, 1838137, 6705494, 24464719, 89204624, 324981985, 1183034546, 4305313447, 15672486692, 57100841641, 208309692974, 761141694367, 2785955603096, 10215141094417

Offset: 0

Author

Paul D. Hanna, May 08 2006

Keywords

• eigen
• nonn

Comments

Self-convolution of A118398, which is also an eigenvector of the triangle defined by T(n,k) = 2^k*C(n,2*k).

Examples

			a(7) = Sum_{k=0..[7/2]} A105070(7,k)*a(k) =
8*(1) + 112*(2) + 224*(7) + 64*(20) = 3080.
		

Crossrefs

Cf. A105070 (triangle), A118398 (A(x)^(1/2)).

Programs

PARI

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

Formula

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).