

A173781


a(n) is the smallest entry of the nth 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
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OFFSET

0,2


COMMENTS

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).


REFERENCES

I. M. Gessel, Super Ballot Numbers, J. Symbolic Computation, 14 (1992), 179194.
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.


LINKS

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


CROSSREFS

Sequence in context: A123411 A244485 A128933 * A106362 A148109 A099216
Adjacent sequences: A173778 A173779 A173780 * A173782 A173783 A173784


KEYWORD

easy,nonn


AUTHOR

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


STATUS

approved



