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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 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: A318987 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 January 19 16:10 EST 2019. Contains 319307 sequences. (Running on oeis4.)