A137686 a(n) = Bigomega(Catalan(n)) - round( 3 n /(2 log(n+2))) (= A081399 - A137687).

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

Offset: 0

Author

M. F. Hasler, Feb 06 2008

Keywords

• easy
• sign

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.

Links

• M. F. Hasler, Table of n, a(n) for n = 0..3000.
• Douglas M. Campbell, The Computation of Catalan Numbers, Mathematics Magazine, Vol. 57, No. 4. (Sep., 1984), pp. 195-208.

Crossrefs

Cf. A000108, A081399, A120626, A137687.

Programs

PARI

A137686(n) = bigomega(prod(i=2,n,(n+i)/i)) - round(3*n/log(n+2)/2)

Formula

a(n) = A001222(A000108(n)).