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%I #6 Sep 18 2021 02:14:22
%S 1,1,1,1,1,1,2,3,4,5,6,8,11,15,20,26,34,45,60,80,107,142,188,249,330,
%T 439,584,776,1030,1366,1813,2408,3199,4249,5642,7490,9944,13204,17534,
%U 23285,30920,41056,54514,72384,96116,127631,169478,225042,298819,396783,526869,699608,928981,1233552
%N Expansion of 1/(1 - x/(1 - x^5/(1 - x^14/(1 - x^30/(1 - x^55/(1 - ... - x^(k*(k+1)*(2*k+1)/6)/(1 - ...))))))), a continued fraction.
%F G.f.: 1/(1 - x/(1 - x^5/(1 - x^14/(1 - x^30/(1 - x^55/(1 - ... - x^A000330(k)/(1 - ...))))))), a continued fraction.
%F a(n) ~ c * d^n, where d = 1.327852426419013789340602526081665378868516025761586390361772232517175463... and c = 0.366619510178622647108505347089605503045273798338613615745637268621... - _Vaclav Kotesovec_, Sep 18 2021
%t nmax = 53; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(k (k + 1) (2 k + 1)/6), 1, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A000330, A206739, A285408, A295072.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Nov 13 2017
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