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A118397 Eigenvector of triangle A105070, where A105070(n,k) = 2^k*C(n+1,2*k+1) for 0<=k<=[n/2], n>=0. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..24.

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).

EXAMPLE

a(7) = Sum_{k=0..[7/2]} A105070(7,k)*a(k) =

8*(1) + 112*(2) + 224*(7) + 64*(20) = 3080.

PROG

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

CROSSREFS

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

Sequence in context: A115117 A029890 A095268 * A171191 A189771 A260504

Adjacent sequences:  A118394 A118395 A118396 * A118398 A118399 A118400

KEYWORD

eigen,nonn

AUTHOR

Paul D. Hanna, May 08 2006

STATUS

approved

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Last modified February 18 05:40 EST 2019. Contains 320245 sequences. (Running on oeis4.)