OFFSET
0,2
COMMENTS
LINKS
Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.
FORMULA
Number triangle T(n,k) = Sum_{j = 0..n} binomial(n+k,j-k)*binomialC(n,j).
T(n,k) = binomial(2*n + k, n + 2*k). - Peter Bala, Nov 24 2015
EXAMPLE
Triangle begins
1,
2, 1,
6, 5, 1,
20, 21, 8, 1,
70, 84, 45, 11, 1,
252, 330, 220, 78, 14, 1,
924, 1287, 1001, 455, 120, 17, 1,
3432, 5005, 4368, 2380, 816, 171, 20, 1
PROG
(Magma) /* As triangle */ [[Binomial(2*n+k, n+2*k): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Nov 27 2015
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Apr 28 2009
STATUS
approved