A285484 - OEIS

%I #6 Aug 26 2017 07:45:16

%S 1,-1,1,-1,2,-3,4,-6,9,-13,18,-26,38,-54,77,-111,160,-229,328,-472,

%T 679,-974,1398,-2010,2888,-4146,5954,-8555,12289,-17647,25346,-36410,

%U 52297,-75109,107881,-154961,222574,-319679,459167,-659528,947295,-1360612,1954295,-2807031,4031809,-5790982

%N G.f.: 1/(1 + x/(1 + x^3/(1 + x^6/(1 + x^10/(1 + x^15/(1 + ... + x^(k*(k+1)/2)/(1 + ...))))))), a continued fraction.

%F a(n) ~ (-1)^n * c * d^n, where d = 1.43632929358192465555987661527... and c = 0.4856490524128736949896673... - _Vaclav Kotesovec_, Aug 26 2017

%e G.f.: A(x) = 1 - x + x^2 - x^3 + 2*x^4 - 3*x^5 + 4*x^6 - 6*x^7 + 9*x^8 - 13*x^9 + ...

%t nmax = 45; CoefficientList[Series[1/(1 + ContinuedFractionK[x^(k (k + 1)/2), 1, {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A000217, A002105, A206740, A285408.

%K sign

%O 0,5

%A _Ilya Gutkovskiy_, Apr 19 2017