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.

1, 1, 4, 9, 128, 675, 2048, 3675, 262144, 3472875, 8388608, 151278435, 268435456, 6249480237, 4294967296, 124351902675, 2199023255552, 15401871374175, 140737488355328, 5834647198969875, 4503599627370496

Offset

1,3

Links

Diana Mecum, Table of n, a(n) for n = 1..100

Formula

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

Example

4! = 24 = 1 + 1/(1 + 1/(-5/4 + 9/44)).
5! = 120 = 1 + 1/(1 + 1/(-5/4 + 1/(44/9 -128/171))).

Crossrefs

Cf. A000142, A128523.

Sequence in context: A168138 A267898 A324981 * A027451 A227744 A035127

Adjacent sequences: A128521 A128522 A128523 * A128525 A128526 A128527

Keyword

frac,nonn

Author

Leroy Quet, Mar 07 2007

Extensions

More terms from Diana L. Mecum, May 29 2007

Status

approved