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%I #11 Sep 26 2017 10:58:33
%S 0,1,2,3,3,4,4,5,5,6,6,6,7,7,8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,
%T 13,13,13,14,14,14,15,15,15,15,16,16,16,17,17,17,18,18,18,18,19,19,19,
%U 20,20,20,20,21,21,21,22,22,22,22,23,23,23,23,24,24,24,25,25,25,25,26,26
%N a(n) = round(3 n / (2 log(n+2))), an approximation to A081399.
%C It is easy to show that A081399(n) is between n/log(n) and 2n/log(n) (for n>n0), cf. [Campbell 1984]. This sequence A137687 is roughly the middle of this interval (with log(n) replaced by log(n+2) to be well-defined for all n>=0), which turns out to be a fair (and simple, increasing) approximation for A081399.
%C See A137686 for the (signed) difference of the two sequences.
%H M. F. Hasler, <a href="/A137687/b137687.txt">Table of n, a(n) for n = 0..3000</a>.
%H Douglas M. Campbell, <a href="http://www.jstor.org/stable/2689673">The Computation of Catalan Numbers</a>, Mathematics Magazine, Vol. 57, No. 4. (Sep., 1984), pp. 195-208.
%o (PARI) A137687(n) = round(3*n/log(n+2)/2) \\ _M. F. Hasler_, Feb 06 2008
%Y Cf. A000108, A001222, A081399, A120626, A137686.
%K easy,nonn
%O 0,3
%A _M. F. Hasler_, Feb 06 2008
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