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A137686
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Bigomega(Catalan(n)) - round( 3 n /(2 log(n+2))) (= A081399 - A137687).
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3
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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.
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REFERENCES
| Douglas M. Campbell, The Computation of Catalan Numbers, Mathematics Magazine, Vol. 57, No. 4. (Sep., 1984), pp. 195-208.
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LINKS
| M. F. Hasler, Table of n, a(n) for n=0,...,3000.
Douglas M. Campbell, The Computation of Catalan Numbers [JSTOR]
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FORMULA
| a(n)=A001222[A000108(n)]
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PROG
| (PARI) A137686(n) = bigomega(prod(i=2, n, (n+i)/i)) - round(3*n/log(n+2)/2)
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CROSSREFS
| Cf. A000108, A081399, A120626, A137687.
Sequence in context: A162642 A139146 A144032 * A143792 A029375 A071462
Adjacent sequences: A137683 A137684 A137685 * A137687 A137688 A137689
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KEYWORD
| easy,sign
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AUTHOR
| M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 06 2008
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