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 A185648 Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=8. 2

%I

%S 1,1,1,2,3,5,9,15,26,45,77,133,230,397,687,1188,2054,3553,6145,10629,

%T 18385,31802,55010,95156,164600,284725,492519,851962,1473732,2549275,

%U 4409764,7628058,13195104,22825046,39483039,68298240,118143130,204365438,353513851

%N Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=8.

%H Alois P. Heinz, <a href="/A185648/b185648.txt">Table of n, a(n) for n = 0..750</a>

%H Paul D. Hanna et al., <a href="http://list.seqfan.eu/pipermail/seqfan/2013-July/011445.html">Formula Needed for a Family of Continued Fractions</a> and follow-up messages on the SeqFan list, Jul 28 2013

%F a(n) ~ c * d^n, where d = 1.729812413755051803149808764090629506945619020643782294236248965..., c = 0.319480257502538464183377228844611044469159258446802374119607096... . - _Vaclav Kotesovec_, Sep 04 2014

%t nMax = 39; col[m_ /; 0 <= m <= nMax] := 1/(1 + ContinuedFractionK[-x^k (1 - x^(m + k)), 1, {k, 1, Ceiling[nMax/2]}]) + O[x]^(2 nMax) // CoefficientList[#, x]&; A185648 = col[8][[1 ;; nMax]] (* _Jean-François Alcover_, Nov 03 2016 *)

%Y Column m=8 of A185646.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Aug 29 2013

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Last modified September 18 19:30 EDT 2021. Contains 347534 sequences. (Running on oeis4.)