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%I #22 Feb 18 2019 05:35:21
%S 1,2,3,5,7,9,11,14,17,20,23,26,29,33,36,40,44,48,52,56,60,65,69,74,78,
%T 83,88,93,98,103,108,114,119,124,130,136,141,147,153,159,165,171,177,
%U 183,189,196,202,209,215,222,229,235,242,249,256,263,270,277,284,292,299,306,314,321,329,336,344,352,360,367,375,383,391,399,408,416,424,432,441,449,457,466,474,483,492,500,509,518,527,536,545,554,563,572,581,590,599,609,618,627,637,646,656,665,675,685,694,704,714,724,734,744,753,764,774,784,794,804,814,825,835,845,856,866,877,887,898,908,919,930,940,951,962,973,984,995,1006
%N a(n) = floor( Catalan(2*n) / Catalan(n)^2 ).
%C This sequence is (roughly) the relative size of the Jones monoid J_n to its minimal ideal. Equivalently, this is roughly the reciprocal of the proportion of Dyck words of length 4n which can be factorized into two Dyck words, each of length 2n.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dyck_word#Applications_in_combinatorics">Dyck word</a>
%F a(n) = floor( Catalan( 2*n ) / Catalan(n)^2 ).
%p Digits:=200:
%p C:=n->binomial(2*n,n)/(n+1); f:=n->floor(C(2*n)/C(n)^2);[seq(f(n),n=0..100)]; # _N. J. A. Sloane_, May 21 2014
%t Table[Floor[CatalanNumber[2n]/CatalanNumber[n]^2],{n,0,140}] (* _Harvey P. Dale_, Oct 04 2015 *)
%Y Cf. A000108.
%K nonn,easy
%O 0,2
%A _Nick Loughlin_, May 01 2014
%E Corrected by _Harvey P. Dale_, Oct 04 2015
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