|
|
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).
S(n,k-n) = C(2k,k) * C(k,n) / C(2k,2n). - Charlie Neder, Dec 27 2018
|
|
LINKS
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Joseph Alfano (jalfano(AT)assumption.edu), Feb 24 2010
|
|
STATUS
|
approved
|
|
|
|