This site is supported by donations to The OEIS Foundation.



Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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



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

Content is available under The OEIS End-User License Agreement .

Last modified November 26 13:40 EST 2014. Contains 250079 sequences.