A295072 - OEIS

%I #7 Sep 18 2021 02:09:57

%S 1,1,1,1,1,2,3,4,5,7,10,14,19,26,36,51,71,98,135,188,262,364,504,699,

%T 971,1350,1874,2600,3608,5011,6959,9661,13409,18615,25846,35887,49821,

%U 69163,96018,133310,185082,256951,356722,495245,687568,954575,1325251,1839865,2554325,3546245,4923342

%N Expansion of 1/(1 - x/(1 - x^4/(1 - x^10/(1 - x^20/(1 - x^35/(1 - ... - x^(k*(k+1)*(k+2)/6)/(1 - ...))))))), a continued fraction.

%F G.f.: 1/(1 - x/(1 - x^4/(1 - x^10/(1 - x^20/(1 - x^35/(1 - ... - x^A000292(k)/(1 - ...))))))), a continued fraction.

%F a(n) ~ c * d^n, where d = 1.388323040709674097023351236945145477752521994116275726548400298175286... and c = 0.369600335108282885310522776855743258910315692223280044555536918225... - _Vaclav Kotesovec_, Sep 18 2021

%t nmax = 50; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(k (k + 1) (k + 2)/6), 1, {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A000292, A206740, A285484, A295073.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Nov 13 2017