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Bigomega(Catalan(n)) - round( 3 n /(2 log(n+2))) (= A081399 - A137687).

+0
3

0, -1, -1, -2, -1, -1, 0, -2, -1, -2, -1, -1, -1, 0, 1, -1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, 1, 0, 1, -2, -1, 0, 0, -2, -1, -1, 1, -1, 0, 2, 2, 2, 2, 1, 3, 1, 2, 0, 2, 1, 1, 1, 1, -1, -1, -1, 1, 0, 2, 3, 3, 0, 0, 0, 1, 0, 3, 2, 2, 0, 2, 3, 3, 2, 2, 3, 4, 1, 0, 1, 1, 1, 1, 1, 3, 1, 4, 2, 2, 1, 2, 2, 3, 2, 3, 1, 2, 0, 1, 0, 2, 1, 2, 2, 3, 1, 3, 2, 3, 1, 2, 3, 3, 2, 3 (list; graph; listen)

	OFFSET	`0,4`
	COMMENT	`It is easy to show that A081399(n) = bigomega(Catalan(n)) is between n/log(n) and 2n/log(n) (for n>n0). The sequence A137687 is roughly the middle of this interval, which turns out to be a fair approximation to A081399. The present sequence lists the (signed) difference.`
	REFERENCES	`Douglas M. Campbell, The Computation of Catalan Numbers, Mathematics Magazine, Vol. 57, No. 4. (Sep., 1984), pp. 195-208.`
	LINKS	`M. F. Hasler, Table of n, a(n) for n=0,...,3000.` `Douglas M. Campbell, The Computation of Catalan Numbers [JSTOR]`
	FORMULA	`a(n)=A001222[A000108(n)]`
	PROGRAM	`(PARI) A137686(n) = bigomega(prod(i=2, n, (n+i)/i)) - round(3*n/log(n+2)/2)`
	CROSSREFS	`Cf. A000108, A081399, A120626, A137687.` `Sequence in context: A125072 A139146 A144032 this_sequence A143792 A029375 A071462` `Adjacent sequences: A137683 A137684 A137685 this_sequence A137687 A137688 A137689`
	KEYWORD	`easy,sign`
	AUTHOR	`M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 06 2008`

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Last modified December 3 01:16 EST 2008. Contains 151161 sequences.

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