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A173781 a(n) is the smallest entry of the n-th column of the matrix of Super Catalan numbers S(m,n). 0
1, 2, 4, 10, 28, 72, 198, 572, 1560, 4420, 12920, 36176, 104006, 305900, 869400, 2521260, 7443720, 21360240, 62300700, 184410072, 532740208 (list; graph; refs; listen; history; text; internal format)



Super Catalan number S(m,n) is [(2m)! (2n)! ] / [(m!) (n!) (m+n)! ], where m,n are nonnegative integers.

S(m,n) is a positive integer, but a combinatorial interpretation of S(m,n) is an open problem.

For each n, the sequence S(m,n) is decreasing then increasing, with minimum value at m = ceiling(n/3).

Our sequence is that list of values S( ceiling(n/3), n).


I. M. Gessel, Super Ballot Numbers, J. Symbolic Computation, 14 (1992), 179-194.

I. M. Gessel and Guoce Xin, A Combinatorial Interpretation of the Numbers 6 (2n)! /n! (n+2)!, J. Integer Seq., 8 (2005), no. 2, Article 05.2.3, 13 pp.


Table of n, a(n) for n=0..20.


Sequence in context: A123411 A244485 A128933 * A106362 A148109 A099216

Adjacent sequences:  A173778 A173779 A173780 * A173782 A173783 A173784




Joseph Alfano (jalfano(AT)assumption.edu), Feb 24 2010



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Last modified December 19 20:59 EST 2014. Contains 252239 sequences.