The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A092276 Triangle read by rows: T(n,k) is the number of noncrossing trees with root degree equal to k. 9
 1, 2, 1, 7, 4, 1, 30, 18, 6, 1, 143, 88, 33, 8, 1, 728, 455, 182, 52, 10, 1, 3876, 2448, 1020, 320, 75, 12, 1, 21318, 13566, 5814, 1938, 510, 102, 14, 1, 120175, 76912, 33649, 11704, 3325, 760, 133, 16, 1, 690690, 444015, 197340, 70840, 21252, 5313, 1078, 168, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS With offset 0, Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A006013. - Philippe Deléham, Jan 23 2010 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 Paul Barry, Characterizations of the Borel triangle and Borel polynomials, arXiv:2001.08799 [math.CO], 2020. 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*binomial(3n-k, n-k)/(3n-k). G.f. = 1/(1-t*z*g^2), where g := 2*sin(arcsin(3*sqrt(3*z)/2)/3)/sqrt(3*z) is the g.f. of the sequence A001764. T(n, k) = Sum_{j, j>=1} j*T(n-1, k-2+j). - Philippe Deléham, Sep 14 2005 With offset 0, T(n,k)= ((n+1)/(k+1))*binomial(3n-k+1, n-k). - Philippe Deléham, Jan 23 2010 Let M = the production matrix 2, 1 3, 2, 1 4, 3, 2, 1 5, 4, 3, 2, 1 ... Top row of M^(n-1) generates n-th row terms of triangle A092276. Leftmost terms of each row = A006013 starting (1, 2, 7, 30, 143,...). - Gary W. Adamson, Jul 07 2011 EXAMPLE Triangle begins:      1;      2,    1;      7,    4,    1;     30,   18,    6,   1;    143,   88,   33,   8,  1;    728,  455,  182,  52, 10,  1;   3876, 2448, 1020, 320, 75, 12, 1;   ... Top row of M^3 = (30, 18, 6, 1) MAPLE T := proc(n, k) if k=n then 1 else 2*k*binomial(3*n-k, n-k)/(3*n-k) fi end: seq(seq(T(n, k), k=1..n), n=1..11); MATHEMATICA t[n_, n_] = 1; t[n_, k_] := 2*k*Binomial[3*n-k, n-k]/(3*n-k); Table[t[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 22 2012, after Maple *) PROG (PARI) T(n, k) = 2*k*binomial(3*n-k, n-k)/(3*n-k); \\ Andrew Howroyd, Nov 06 2017 CROSSREFS Row sums give sequence A001764. Columns 1..5 are A006013, A006629, A006630, A006631, A233657. Sequence in context: A072248 A317360 A177011 * A011274 A122843 A167196 Adjacent sequences:  A092273 A092274 A092275 * A092277 A092278 A092279 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Feb 24 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 21 08:31 EST 2021. Contains 340338 sequences. (Running on oeis4.)