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A168441 Expansion of 1/(1-x/(1-2x/(1-4x/(1-6x/(1-8x/(1-.... (continued fraction). 2
1, 1, 3, 17, 155, 2025, 34819, 743329, 18937707, 560071193, 18844479635, 710440531665, 29654234779771, 1357326276747721, 67589738142784803, 3637403230889380097, 210358430818676801675, 13009719599952748481145 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is A168442.

LINKS

Table of n, a(n) for n=0..17.

FORMULA

G.f.: 1/(1-x-2x^2/(1-6x-24x^2/(1-14x-80x^2/(1-22x-168x^2/(1-30x-288x^2/(1-... (continued fraction).

a(n)= Sum_{k, 0<=k<=n} A111106(n,k)*2^(n-k). [From Philippe Deléham, Nov 28 2009]

a(n) = upper left term of M^n, M = an infinite square production matrix as follows:

1, 1, 0, 0, 0, 0,...

2, 2, 2, 0, 0, 0,...

4, 4, 4, 4, 0, 0,...

6, 6, 6, 6, 6, 0,...

8, 8, 8, 8, 8, 8,...

...

(where the series (1,2,4,6,8,...) = A004277, positive even integers prefaced with a 1.) - Gary W. Adamson, Jul 19 2011

G.f. A(x) = 1+x/(G(0)-x) where G(k)= 1 - x*(2*k+2)/G(k+1)); (continued fraction, 1-step).- Sergei N. Gladkovskii, Oct 28 2012

CROSSREFS

Sequence in context: A193161 A208832 A135751 * A001469 A110501 A274539

Adjacent sequences:  A168438 A168439 A168440 * A168442 A168443 A168444

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 25 2009

STATUS

approved

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Last modified October 18 01:01 EDT 2018. Contains 316297 sequences. (Running on oeis4.)