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 A101449 Triangle read by rows: T(n,k) is number of noncrossing trees with n edges and having k nonroot nodes of degree 1. 3
 1, 1, 2, 4, 4, 4, 11, 24, 12, 8, 41, 88, 96, 32, 16, 146, 410, 440, 320, 80, 32, 564, 1752, 2460, 1760, 960, 192, 64, 2199, 7896, 12264, 11480, 6160, 2688, 448, 128, 8835, 35184, 63168, 65408, 45920, 19712, 7168, 1024, 256, 35989, 159030, 316656, 379008 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row n contains n terms. Row sums yield the ternary numbers (A001764). The average number of nonroot nodes of degree 1 over all noncrossing trees with n edges is 4n(n-1)(2n+1)/(3(3n-1)(3n-2)) ~ 8n/27. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math., 204, 203-229, 1999. M. Noy, Enumeration of noncrossing trees on a circle, Discrete Math., 180, 301-313, 1998. FORMULA T(n, k) = [2^k/(n-k)]*binomial(n-1, k)*Sum_{i=1..n-k} (-1)^(n-k-i)*2^(n-k-i)*binomial(n-k, i)*binomial(3i, i-1), 0 <= k < n). T(n,k) = 2^k*binomial(n-1,k)*A030981(n-k). EXAMPLE T(2,0)=1 (/\); T(2,1)=2 (/_, _\ ). Triangle begins:    1;    1,  2;    4,  4,  4;   11, 24, 12,  8;   41, 88, 96, 32, 16; MAPLE T:=proc(n, k) if k

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Last modified April 5 16:49 EDT 2020. Contains 333245 sequences. (Running on oeis4.)