OFFSET
1,5
COMMENTS
Table starts
.1...1.....1........1...........1..............1.................1
.1...2.....3........6..........10.............20................35
.1...3.....6.......30..........70............420..............1050
.1...6....30......280........2100..........23100............210210
.1..10....70.....2100.......23100........1051050..........14294280
.1..20...420....23100.....1051050.......85765680........5703417720
.1..35..1050...210210....14294280.....5703417720......577185873264
.1..70..6930..2522520...814773960...577185873264...337653735859440
.1.126.18018.25729704.12547518984.48236247979920.43364386933948080
Even columns match A215292.
The first column is number of symmetric standard Young tableaux of shape (n), the second column is number of symmetric standard Young tableaux of shape (n,n) and the third column is number of symmetric standard Young tableaux of shape (n,n,n). - Ran Pan, May 21 2015
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..1000
Hodge, Jonathan K.; Krines, Mark; Lahr, Jennifer, Preseparable extensions of multidimensional preferences, Order 26, No. 2, 125-147 (2009), Table 1.
Ran Pan, Exercise P, Problem 4, Project P.
FORMULA
EXAMPLE
Some solutions for n=5, k=4:
..x..0..x..4....x..0..x..1....x..1..x..3....x..0..x..6....x..0..x..1
..1..x..2..x....4..x..7..x....0..x..8..x....3..x..5..x....3..x..7..x
..x..3..x..8....x..2..x..3....x..2..x..5....x..1..x..7....x..2..x..5
..6..x..7..x....5..x..9..x....4..x..9..x....4..x..9..x....6..x..8..x
..x..5..x..9....x..6..x..8....x..6..x..7....x..2..x..8....x..4..x..9
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 07 2012
STATUS
approved