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A302285 Expansion of 1/(1 - x - x/(1 - 2*x - x/(1 - 3*x - x/(1 - 4*x - x/(1 - 5*x - x/(1 - ...)))))), a continued fraction. 0

%I

%S 1,2,7,33,185,1170,8121,60846,486753,4125852,36846557,345205559,

%T 3381126995,34524194712,366635359887,4041180951473,46149726728969,

%U 545161967955668,6652026230285141,83730953689450825,1085924693069106823,14494802798426546660,198918641942013097723

%N Expansion of 1/(1 - x - x/(1 - 2*x - x/(1 - 3*x - x/(1 - 4*x - x/(1 - 5*x - x/(1 - ...)))))), a continued fraction.

%e G.f. A(x) = 1 + 2*x + 7*x^2 + 33*x^3 + 185*x^4 + 1170*x^5 + 8121*x^6 + 60846*x^7 + 486753*x^8 + ...

%t nmax = 22; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-x, 1 - (k + 1) x, {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A001515, A006318, A006351, A006789, A258173, A295289.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 04 2018

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Last modified April 15 08:58 EDT 2021. Contains 342977 sequences. (Running on oeis4.)