A295944 - OEIS

%I #9 Sep 24 2020 02:56:48

%S 1,1,2,9,48,330,2760,26670,295680,3686760,51080400,778516200,

%T 12944131200,233156523600,4522777459200,94000269963600,

%U 2083918752115200,49086474041404800,1224240044169542400,32229413145084355200,893129953569780326400,25987602379142314310400,792175050968260985625600

%N Expansion of e.g.f. 1/(1 - x/(1 - x^2/(2 - x^3/(3 - x^4/(4 - x^5/(5 - x^6/(6 - x^7/(7 - ...)))))))), a continued fraction.

%H Vaclav Kotesovec, <a href="/A295944/b295944.txt">Table of n, a(n) for n = 0..300</a>

%F a(n) ~ c * d^n * n!, where d = 1.38558212161941692858602713469062337279193542118277136584639901149123656221... and c = 0.53969028910223464320214486945875671476165137860949073877514057198146... - _Vaclav Kotesovec_, Sep 24 2020

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

%Y Cf. A005169, A181167, A257544, A295945.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Nov 30 2017