A128524 - OEIS

A128524

a(n) = denominator of r(n): r(n) is such that the continued fraction (of rational terms) [r(1);r(2),...r(n)] equals n! for every positive integer n.

%I #9 Apr 09 2014 10:13:42

%S 1,1,4,9,128,675,2048,3675,262144,3472875,8388608,151278435,268435456,

%T 6249480237,4294967296,124351902675,2199023255552,15401871374175,

%U 140737488355328,5834647198969875,4503599627370496

%N a(n) = denominator of r(n): r(n) is such that the continued fraction (of rational terms) [r(1);r(2),...r(n)] equals n! for every positive integer n.

%H Diana Mecum, <a href="/A128524/b128524.txt">Table of n, a(n) for n = 1..100</a>

%F For n >= 4, r(n) = -(n - 1/(n-1)) *(n + 1/(n-3)) /(r(n-1) (n-1)).

%e 4! = 24 = 1 + 1/(1 + 1/(-5/4 + 9/44)).

%e 5! = 120 = 1 + 1/(1 + 1/(-5/4 + 1/(44/9 -128/171))).

%Y Cf. A000142, A128523.

%K frac,nonn

%O 1,3

%A _Leroy Quet_, Mar 07 2007

%E More terms from _Diana L. Mecum_, May 29 2007