A291274 - OEIS

%I #31 Feb 16 2025 08:33:50

%S 1,1,4,36,384,5125,81864,1519833,32219136,768352149,20367510000,

%T 594270942705,18929706034176,653744865197242,24333393186194848,

%U 971177936039212500,41376191798281502720,1874320475909920820607,89961819584112859211712,4560744533588836253021837

%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="https://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>

%F a(n) = A286933(n,n).

%F a(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 A286933.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Aug 22 2017