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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). 1
1, 2, 4, 10, 28, 72, 198, 572, 1560, 4420, 12920, 36176, 104006, 305900, 869400, 2521260, 7443720, 21360240, 62300700, 184410072, 532740208, 1560167752, 4626704368, 13432367520, 39457579590, 117177054540, 341487416088, 1005490725148, 2989296750440, 8737944347440, 25776935824948 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..2099

Ira M. Gessel, Super ballot numbers, J. Symbolic Comp., 14 (1992), 179-194

Ira M. Gessel and Guoce Xin, A Combinatorial Interpretation of the Numbers 6(2n)!/n!(n+2)!, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.3, 13 pp.

MATHEMATICA

nn = 30; {1}~Join~Table[Min@ Map[Function[n, ((2 m)! (2 n)!)/((m!) (n!) (m + n)!)], Range@ nn], {m, nn}] (* Michael De Vlieger, Jul 16 2016 *)

CROSSREFS

Sequence in context: A278418 A244485 A128933 * A106362 A271896 A148109

Adjacent sequences:  A173778 A173779 A173780 * A173782 A173783 A173784

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified December 8 06:50 EST 2016. Contains 278902 sequences.