OFFSET
0,3
COMMENTS
This triangle forms a companion to A119245.
Combinatorial interpretations of T(n,k):
1) The number of standard tableaux of shape (n-2*k-1,n+2*k+1).
2) The entries in column k are (with an offset of 2*k+1) the number of n-th generation vertices in the tree of sequences with unit increase labeled by 4*k+2. See [Sunik, Theorem 4].
LINKS
Zoran Sunic, Self describing sequences and the Catalan family tree, Elect. J. Combin., 10 (No. 1, 2003).
FORMULA
EXAMPLE
Triangle begins
==================================
n\k|.....0.....1.....2.....3.....4
==================================
.0.|.....0
.1.|.....1
.2.|.....3
.3.|.....9.....1
.4.|....28.....7
.5.|....90....35.....1
.6.|...297...154....11
.7.|..1001...637....77.....1
.8.|..3432..2548...440....15
.9.|.11934..9996..2244...135.....1
MAPLE
with(combinat): T:=(n, k) -> (4k+3)/(n+2k+2)*binomial(2n, n+2k+1): for n from 0 to 13 do seq(T(n, k), k = 0..6); end do;
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Peter Bala, Mar 20 2009
STATUS
approved