login
a(n) = [x^n] 1/(1 + n*x/(1 + n*x^2/(1 + n*x^3/(1 + n*x^4/(1 + n*x^5/(1 - ...)))))), a continued fraction.
2

%I #6 Aug 26 2017 07:17:34

%S 1,-1,4,-18,128,-1375,19224,-328937,6594560,-150804585,3866510000,

%T -109763181693,3416538258432,-115680589167780,4232540747232224,

%U -166402907912306250,6995675389431382016,-313160900844718102493,14871520058618111804352,-746718033885917073001959

%N a(n) = [x^n] 1/(1 + n*x/(1 + n*x^2/(1 + n*x^3/(1 + n*x^4/(1 + n*x^5/(1 - ...)))))), a continued fraction.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>

%F a(n) = A286932(n,n).

%F a(n) ~ (-1)^n * exp(-1) * n^n. - _Vaclav Kotesovec_, Aug 26 2017

%t Table[SeriesCoefficient[1/(1 + ContinuedFractionK[n x^i, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 19}]

%Y Main diagonal of A286932.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Aug 22 2017