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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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

LINKS

Table of n, a(n) for n=0..25.

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).

EXAMPLE

a(7) = Sum_{k=0..[7/2]} 2^k*C(7,2*k)*a(k) =

1*(1) + 42*(1) + 140*(3) + 56*(7) = 855.

PROG

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

CROSSREFS

Cf. A118397 (self-convolution).

Sequence in context: A148734 A124425 A321606 * A047974 A148735 A148736

Adjacent sequences:  A118395 A118396 A118397 * A118399 A118400 A118401

KEYWORD

eigen,nonn

AUTHOR

Paul D. Hanna, May 08 2006

STATUS

approved

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Last modified March 18 16:27 EDT 2019. Contains 321292 sequences. (Running on oeis4.)