A128523 - OEIS

A128523

a(n) = numerator 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, -5, 44, -171, 3712, -3075, 22528, -434875, 23330816, -15141735, 1098907648, -521070165, 48586817536, -8885315439, 1026497183744, -4814195089275, 134140418588672, -324199885098375, 53339508086669312

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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, A128524.

Sequence in context: A262118 A173376 A364605 * A366650 A271298 A271118

Adjacent sequences: A128520 A128521 A128522 * A128524 A128525 A128526

KEYWORD

frac,sign

AUTHOR

Leroy Quet, Mar 07 2007

EXTENSIONS

More terms from Diana L. Mecum, Jun 15 2007

STATUS

approved