id:A128523 - OEIS Search Results

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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.

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1, 1, -5, 44, -171, 3712, -3075, 22528, -434875, 23330816, -15141735, 1098907648, -521070165, 48586817536, -8885315439, 1026497183744, -4814195089275, 134140418588672, -324199885098375, 53339508086669312 (list; graph; listen)

	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: A030698 A080284 A071861 this_sequence A068311 A109984 A096355` `Adjacent sequences: A128520 A128521 A128522 this_sequence A128524 A128525 A128526`
	KEYWORD	`frac,sign`
	AUTHOR	`Leroy Quet (qq-quet(AT)mindspring.com), Mar 07 2007`
	EXTENSIONS	`More terms from Diana Mecum (diana.mecum(AT)gmail.com), Jun 15 2007`

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Last modified August 29 17:54 EDT 2008. Contains 143238 sequences.

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